Lattice Path Combinatorics And Special Counting Sequences

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Lattice Path Combinatorics and Special Counting Sequences

Author : Chunwei Song
Publisher : CRC Press
ISBN 13 : 1040123414
Total Pages : 120 pages
Book Rating : 4.0/5 (41 download)

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Book Synopsis Lattice Path Combinatorics and Special Counting Sequences by : Chunwei Song

Download or read book Lattice Path Combinatorics and Special Counting Sequences written by Chunwei Song and published by CRC Press. This book was released on 2024-09-17 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book endeavors to deepen our understanding of lattice path combinatorics, explore key types of special sequences, elucidate their interconnections, and concurrently champion the author's interpretation of the “combinatorial spirit”. The author intends to give an up-to-date introduction to the theory of lattice path combinatorics, its relation to those special counting sequences important in modern combinatorial studies, such as the Catalan, Schröder, Motzkin, Delannoy numbers, and their generalized versions. Brief discussions of applications of lattice path combinatorics to symmetric functions and connections to the theory of tableaux are also included. Meanwhile, the author also presents an interpretation of the "combinatorial spirit" (i.e., "counting without counting", bijective proofs, and understanding combinatorics from combinatorial structures internally, and more), hoping to shape the development of contemporary combinatorics. Lattice Path Combinatorics and Special Counting Sequences: From an Enumerative Perspective will appeal to graduate students and advanced undergraduates studying combinatorics, discrete mathematics, or computer science.

Lattice Path Counting and Applications

Author : Gopal Mohanty
Publisher : Academic Press
ISBN 13 : 1483218805
Total Pages : 200 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Lattice Path Counting and Applications by : Gopal Mohanty

Download or read book Lattice Path Counting and Applications written by Gopal Mohanty and published by Academic Press. This book was released on 2014-07-10 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Lattice Path Counting and Applications focuses on the principles, methodologies, and approaches involved in lattice path counting and applications, including vector representation, random walks, and rank order statistics. The book first underscores the simple and general boundaries of path counting. Topics include types of diagonal steps and a correspondence, paths within general boundaries, higher dimensional paths, vector representation, compositions, and domination, recurrence and generating function method, and reflection principle. The text then examines invariance and fluctuation and random walk and rank order statistics. Discussions focus on random walks, rank order statistics, Chung-Feller theorems, and Sparre Andersen's equivalence. The manuscript takes a look at convolution identities and inverse relations and discrete distributions, queues, trees, and search codes, as well as discrete distributions and a correlated random walk, trees and search codes, convolution identities, and orthogonal relations and inversion formulas. The text is a valuable reference for mathematicians and researchers interested in in lattice path counting and applications.

Lattice Path Combinatorics and Applications

Author : George E. Andrews
Publisher : Springer
ISBN 13 : 3030111024
Total Pages : 418 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Lattice Path Combinatorics and Applications by : George E. Andrews

Download or read book Lattice Path Combinatorics and Applications written by George E. Andrews and published by Springer. This book was released on 2019-03-02 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most recent methods in various branches of lattice path and enumerative combinatorics along with relevant applications are nicely grouped together and represented in this research contributed volume. Contributions to this edited volume will be mainly research articles however it will also include several captivating, expository articles (along with pictures) on the life and mathematical work of leading researchers in lattice path combinatorics and beyond. There will be four or five expository articles in memory of Shreeram Shankar Abhyankar and Philippe Flajolet and honoring George Andrews and Lajos Takács. There may be another brief article in memory of Professors Jagdish Narayan Srivastava and Joti Lal Jain. New research results include the kernel method developed by Flajolet and others for counting different classes of lattice paths continues to produce new results in counting lattice paths. The recent investigation of Fishburn numbers has led to interesting counting interpretations and a family of fascinating congruences. Formulas for new methods to obtain the number of Fq-rational points of Schubert varieties in Grassmannians continues to have research interest and will be presented here. Topics to be included are far reaching and will include lattice path enumeration, tilings, bijections between paths and other combinatoric structures, non-intersecting lattice paths, varieties, Young tableaux, partitions, enumerative combinatorics, discrete distributions, applications to queueing theory and other continuous time models, graph theory and applications. Many leading mathematicians who spoke at the conference from which this volume derives, are expected to send contributions including. This volume also presents the stimulating ideas of some exciting newcomers to the Lattice Path Combinatorics Conference series; “The 8th Conference on Lattice Path Combinatorics and Applications” provided opportunities for new collaborations; some of the products of these collaborations will also appear in this book. This book will have interest for researchers in lattice path combinatorics and enumerative combinatorics. This will include subsets of researchers in mathematics, statistics, operations research and computer science. The applications of the material covered in this edited volume extends beyond the primary audience to scholars interested queuing theory, graph theory, tiling, partitions, distributions, etc. An attractive bonus within our book is the collection of special articles describing the top recent researchers in this area of study and documenting the interesting history of who, when and how these beautiful combinatorial results were originally discovered.

Counting Lattice Paths Using Fourier Methods

Author : Shaun Ault
Publisher : Springer Nature
ISBN 13 : 3030266966
Total Pages : 136 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Counting Lattice Paths Using Fourier Methods by : Shaun Ault

Download or read book Counting Lattice Paths Using Fourier Methods written by Shaun Ault and published by Springer Nature. This book was released on 2019-08-30 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph introduces a novel and effective approach to counting lattice paths by using the discrete Fourier transform (DFT) as a type of periodic generating function. Utilizing a previously unexplored connection between combinatorics and Fourier analysis, this method will allow readers to move to higher-dimensional lattice path problems with ease. The technique is carefully developed in the first three chapters using the algebraic properties of the DFT, moving from one-dimensional problems to higher dimensions. In the following chapter, the discussion turns to geometric properties of the DFT in order to study the corridor state space. Each chapter poses open-ended questions and exercises to prompt further practice and future research. Two appendices are also provided, which cover complex variables and non-rectangular lattices, thus ensuring the text will be self-contained and serve as a valued reference. Counting Lattice Paths Using Fourier Methods is ideal for upper-undergraduates and graduate students studying combinatorics or other areas of mathematics, as well as computer science or physics. Instructors will also find this a valuable resource for use in their seminars. Readers should have a firm understanding of calculus, including integration, sequences, and series, as well as a familiarity with proofs and elementary linear algebra.

Analytic Combinatorics

Author : Philippe Flajolet
Publisher : Cambridge University Press
ISBN 13 : 1139477161
Total Pages : 825 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Analytic Combinatorics by : Philippe Flajolet

Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Model Theoretic Methods in Finite Combinatorics

Author : Martin Grohe
Publisher : American Mathematical Soc.
ISBN 13 : 0821849433
Total Pages : 529 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Model Theoretic Methods in Finite Combinatorics by : Martin Grohe

Download or read book Model Theoretic Methods in Finite Combinatorics written by Martin Grohe and published by American Mathematical Soc.. This book was released on 2011-11-28 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS-ASL Special Session on Model Theoretic Methods in Finite Combinatorics, held January 5-8, 2009, in Washington, DC. Over the last 20 years, various new connections between model theory and finite combinatorics emerged. The best known of these are in the area of 0-1 laws, but in recent years other very promising interactions between model theory and combinatorics have been developed in areas such as extremal combinatorics and graph limits, graph polynomials, homomorphism functions and related counting functions, and discrete algorithms, touching the boundaries of computer science and statistical physics. This volume highlights some of the main results, techniques, and research directions of the area. Topics covered in this volume include recent developments on 0-1 laws and their variations, counting functions defined by homomorphisms and graph polynomials and their relation to logic, recurrences and spectra, the logical complexity of graphs, algorithmic meta theorems based on logic, universal and homogeneous structures, and logical aspects of Ramsey theory.

An Invitation to Combinatorics

Author : Shahriar Shahriari
Publisher : Cambridge University Press
ISBN 13 : 1108756425
Total Pages : 636 pages
Book Rating : 4.1/5 (87 download)

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Book Synopsis An Invitation to Combinatorics by : Shahriar Shahriari

Download or read book An Invitation to Combinatorics written by Shahriar Shahriari and published by Cambridge University Press. This book was released on 2021-07-22 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: Active student engagement is key to this classroom-tested combinatorics text, boasting 1200+ carefully designed problems, ten mini-projects, section warm-up problems, and chapter opening problems. The author – an award-winning teacher – writes in a conversational style, keeping the reader in mind on every page. Students will stay motivated through glimpses into current research trends and open problems as well as the history and global origins of the subject. All essential topics are covered, including Ramsey theory, enumerative combinatorics including Stirling numbers, partitions of integers, the inclusion-exclusion principle, generating functions, introductory graph theory, and partially ordered sets. Some significant results are presented as sets of guided problems, leading readers to discover them on their own. More than 140 problems have complete solutions and over 250 have hints in the back, making this book ideal for self-study. Ideal for a one semester upper undergraduate course, prerequisites include the calculus sequence and familiarity with proofs.

Combinatorics '90

Author : A. Barlotti
Publisher : Elsevier
ISBN 13 : 0080867928
Total Pages : 577 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Combinatorics '90 by : A. Barlotti

Download or read book Combinatorics '90 written by A. Barlotti and published by Elsevier. This book was released on 1992-08-17 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume forms a valuable source of information on recent developments in research in combinatorics, with special regard to the geometric point of view. Topics covered include: finite geometries (arcs, caps, special varieties in a Galois space; generalized quadrangles; Benz planes; foundation of geometry), partial geometries, Buekenhout geometries, transitive permutation sets, flat-transitive geometries, design theory, finite groups, near-rings and semifields, MV-algebras, coding theory, cryptography and graph theory in its geometric and design aspects.

An Invitation to Analytic Combinatorics

Author : Stephen Melczer
Publisher : Springer Nature
ISBN 13 : 3030670805
Total Pages : 418 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis An Invitation to Analytic Combinatorics by : Stephen Melczer

Download or read book An Invitation to Analytic Combinatorics written by Stephen Melczer and published by Springer Nature. This book was released on 2020-12-22 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains. After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theory can help refine some of these computability questions. Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text.

Algebraic Combinatorics and Computer Science

Author : H. Crapo
Publisher : Springer Science & Business Media
ISBN 13 : 8847021073
Total Pages : 542 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis Algebraic Combinatorics and Computer Science by : H. Crapo

Download or read book Algebraic Combinatorics and Computer Science written by H. Crapo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, dedicated to the memory of Gian-Carlo Rota, is the result of a collaborative effort by his friends, students and admirers. Rota was one of the great thinkers of our times, innovator in both mathematics and phenomenology. I feel moved, yet touched by a sense of sadness, in presenting this volume of work, despite the fear that I may be unworthy of the task that befalls me. Rota, both the scientist and the man, was marked by a generosity that knew no bounds. His ideas opened wide the horizons of fields of research, permitting an astonishing number of students from all over the globe to become enthusiastically involved. The contagious energy with which he demonstrated his tremendous mental capacity always proved fresh and inspiring. Beyond his renown as gifted scientist, what was particularly striking in Gian-Carlo Rota was his ability to appreciate the diverse intellectual capacities of those before him and to adapt his communications accordingly. This human sense, complemented by his acute appreciation of the importance of the individual, acted as a catalyst in bringing forth the very best in each one of his students. Whosoever was fortunate enough to enjoy Gian-Carlo Rota's longstanding friendship was most enriched by the experience, both mathematically and philosophically, and had occasion to appreciate son cote de bon vivant. The book opens with a heartfelt piece by Henry Crapo in which he meticulously pieces together what Gian-Carlo Rota's untimely demise has bequeathed to science.

Combinatorics: The Art of Counting

Author : Bruce E. Sagan
Publisher : American Mathematical Soc.
ISBN 13 : 1470460327
Total Pages : 304 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Combinatorics: The Art of Counting by : Bruce E. Sagan

Download or read book Combinatorics: The Art of Counting written by Bruce E. Sagan and published by American Mathematical Soc.. This book was released on 2020-10-16 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.

Enumerative Combinatorics

Author : Richard Stanley
Publisher : Cambridge University Press
ISBN 13 : 1009262491
Total Pages : 801 pages
Book Rating : 4.0/5 (92 download)

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Book Synopsis Enumerative Combinatorics by : Richard Stanley

Download or read book Enumerative Combinatorics written by Richard Stanley and published by Cambridge University Press. This book was released on 2023-08-17 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revised second volume of the standard guide to enumerative combinatorics, including the theory of symmetric functions and 159 new exercises.

Enumerative Combinatorics: Volume 1

Author : Richard P. Stanley
Publisher : Cambridge University Press
ISBN 13 : 1107015421
Total Pages : 641 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Enumerative Combinatorics: Volume 1 by : Richard P. Stanley

Download or read book Enumerative Combinatorics: Volume 1 written by Richard P. Stanley and published by Cambridge University Press. This book was released on 2012 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets.

Combinatorial Mathematics VIII

Author : K. L. McAvaney
Publisher : Springer
ISBN 13 : 3540387927
Total Pages : 377 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Combinatorial Mathematics VIII by : K. L. McAvaney

Download or read book Combinatorial Mathematics VIII written by K. L. McAvaney and published by Springer. This book was released on 2006-11-14 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Counting Pairs of Lattice Paths by Intersections

Author : Gessel, Ira
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (358 download)

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Book Synopsis Counting Pairs of Lattice Paths by Intersections by : Gessel, Ira

Download or read book Counting Pairs of Lattice Paths by Intersections written by Gessel, Ira and published by . This book was released on 1994 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Combinatorics

Author : Nicholas Loehr
Publisher : CRC Press
ISBN 13 : 149878027X
Total Pages : 849 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Combinatorics by : Nicholas Loehr

Download or read book Combinatorics written by Nicholas Loehr and published by CRC Press. This book was released on 2017-08-10 with total page 849 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics, Second Edition is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics. Part I of the second edition develops an array of mathematical tools to solve counting problems: basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear algebraic methods. These tools are used to analyze combinatorial structures such as words, permutations, subsets, functions, graphs, trees, lattice paths, and much more. Part II cover topics in algebraic combinatorics including group actions, permutation statistics, symmetric functions, and tableau combinatorics. This edition provides greater coverage of the use of ordinary and exponential generating functions as a problem-solving tool. Along with two new chapters, several new sections, and improved exposition throughout, the textbook is brimming with many examples and exercises of various levels of difficulty.

Number Theory and Combinatorics

Author : Bruce M. Landman
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110754266
Total Pages : 388 pages
Book Rating : 4.1/5 (17 download)

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Book Synopsis Number Theory and Combinatorics by : Bruce M. Landman

Download or read book Number Theory and Combinatorics written by Bruce M. Landman and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-04-19 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over a career that spanned 60 years, Ronald L. Graham (known to all as Ron) made significant contributions to the fields of discrete mathematics, number theory, Ramsey theory, computational geometry, juggling and magical mathematics, and many more. Ron also was a mentor to generations of mathematicians, he gave countless talks and helped bring mathematics to a wider audience, and he held signifi cant leadership roles in the mathematical community. This volume is dedicated to the life and memory of Ron Graham, and includes 20-articles by leading scientists across a broad range of subjects that refl ect some of the many areas in which Ron worked.