Counting Lattice Paths Using Fourier Methods
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Counting Lattice Paths Using Fourier Methods
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Author : Shaun Ault
language : en
Publisher: Springer Nature
Release Date : 2019-08-30
Counting Lattice Paths Using Fourier Methods written by Shaun Ault and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-30 with Mathematics categories.
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.
Lattice Path Combinatorics And Special Counting Sequences
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Author : Chunwei Song
language : en
Publisher: CRC Press
Release Date : 2024-09-17
Lattice Path Combinatorics And Special Counting Sequences written by Chunwei Song and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-17 with Mathematics categories.
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.
2nd Ima Conference On Mathematics Of Robotics
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Author : William Holderbaum
language : en
Publisher: Springer Nature
Release Date : 2021-11-20
2nd Ima Conference On Mathematics Of Robotics written by William Holderbaum and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-20 with Technology & Engineering categories.
This book highlights the mathematical depth and sophistication of techniques used in different areas of robotics. Each chapter is a peer-reviewed version of a paper presented during the 2021 IMA Conference on the Mathematics of Robotics, held online September 8–10, 2021. The conference gave a platform to researchers with fundamental contributions and for academic and to share new ideas. The book illustrates some of the current interest in advanced mathematics and robotics such as algebraic geometry, tropical geometry, monodromy and homotopy continuation methods applied to areas such as kinematics, path planning, swam robotics, dynamics and control. It is hoped that the conference and this publications will stimulate further related mathematical research in robotics.
Lattice Path Counting And Applications
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Author : Gopal Mohanty
language : en
Publisher: Academic Press
Release Date : 2014-07-10
Lattice Path Counting And Applications written by Gopal Mohanty and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.
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.
Techniques Of Counting
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Author : Richard Johnson
language : en
Publisher: HiTeX Press
Release Date : 2025-06-20
Techniques Of Counting written by Richard Johnson and has been published by HiTeX Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-20 with Computers categories.
"Techniques of Counting" "Techniques of Counting" is a comprehensive and authoritative guide that delves deeply into the art and science of enumeration, a cornerstone of combinatorics and discrete mathematics. The book commences with a meticulous treatment of fundamental counting principles—such as the sum and product rules, permutations, combinations, and critical axioms like the pigeonhole principle and inclusion-exclusion. Through crisp exposition and illustrative examples, the early chapters lay a robust groundwork, equipping readers with the essential tools needed for both elementary and intricate counting scenarios, all while seamlessly connecting to the broader framework of set theory and combinatorial identities. Building on this foundation, the text skillfully navigates advanced topics including generating functions, recurrence relations, and a rich array of combinatorial structures such as multinomials, Stirling and Bell numbers, Catalan numbers, and Ferrers diagrams. It ventures further into specialized domains, providing thorough coverage of graph enumeration, group-theoretic methods, and analytic tools like asymptotics and singularity analysis. Readers are introduced to elegant algebraic techniques, probabilistic methods, and the challenges of counting within complexity theory, with dedicated chapters on the computational hardness of counting problems, approximate algorithms, and the subtleties of constraint-based enumeration. The final chapters broaden the book’s relevance by surveying real-world applications across diverse fields. These range from error-correcting codes and cryptographic protocols to statistical mechanics, bioinformatics, and machine learning, illustrating the versatility and profound utility of combinatorial enumeration in both theory and practice. Whether for students eager to master foundational techniques or researchers seeking advanced insights, "Techniques of Counting" stands as an indispensable reference—a lucid and exhaustive resource for anyone fascinated by the universe of counting.
Explorations In Complex And Riemannian Geometry
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Author : John Bland
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Explorations In Complex And Riemannian Geometry written by John Bland and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This book contains contributions by an impressive list of leading mathematicians. The articles include high-level survey and research papers exploring contemporary issues in geometric analysis, differential geometry, and several complex variables. Many of the articles will provide graduate students with a good entry point into important areas of modern research. The material is intended for researchers and graduate students interested in several complex variables and complex geometry.
College Of Engineering
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Author : University of Michigan. College of Engineering
language : en
Publisher: UM Libraries
Release Date : 1990
College Of Engineering written by University of Michigan. College of Engineering and has been published by UM Libraries this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Engineering schools categories.
A Course On Queueing Models
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Author : Joti Lal Jain
language : en
Publisher: CRC Press
Release Date : 2006-07-20
A Course On Queueing Models written by Joti Lal Jain and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-20 with Mathematics categories.
The application of engineering principles in divergent fields such as management science and communications as well as the advancement of several approaches in theory and computation have led to growing interest in queueing models, creating the need for a comprehensive text. Emphasizing Markovian structures and the techniques that occur in different models, A Course on Queueing Models discusses recent developments in the field, different methodological tools - some of which are not available elsewhere - and computational techniques. While most books essentially address the classical methods of queueing theory, this text covers a broad range of methods both in theory and in computation. The first part of the textbook exposes you to many fundamental concepts at an introductory level and provides tools for practitioners. It discusses the basics in queueing theory for Markovian and regenerative non-Markovian models, statistical inference, simulation and some computational procedures, network and discrete-time queues, algebraic and combinatorial methods, and optimization. The second part delves deeper into the topics examined in the first part by presenting more advanced methods. This part also includes general queues, duality in queues, and recent advancements on computational methods and discrete-time queues. Each chapter contains a discussion section that summarizes material and highlights special features. Incorporating different queueing models, A Course on Queueing Models achieves an ideal balance between theory and practice, making it compatible for advanced undergraduate and graduate students, applied statisticians, and engineers.
Annales De L Institut Fourier
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Author :
language : en
Publisher:
Release Date : 2005
Annales De L Institut Fourier written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Suprematism In Harmonic Analysis
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Author : Antonio Córdoba
language : en
Publisher: Springer Nature
Release Date : 2024-11-08
Suprematism In Harmonic Analysis written by Antonio Córdoba and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-08 with Mathematics categories.
This award-winning monograph explores advanced topics in harmonic analysis, addressing both classical and contemporary problems. Several connections to number theory, crystallography or atomic theory are also surveyed. The term “suprematism” refers to a certain geometric point of view underlying proofs and arguments. The opening of the book is dedicated to a few results, with short statements and proofs, that could be called “mathematical haikus”. Then, in the first part of the book, singular integrals beyond the classical Calderón-Zygmund theory, such as Vitali-type covering lemmas and estimates for the corresponding maximal operators, are explored. The exponential overlapping of parallelepipeds, the strong maximal function, and Zygmund's conjecture about monotonic bases are also covered. The core of this part is devoted to the Kakeya maximal function and its relation to the spherical summation of Fourier series and integrals. The two-dimensional case is well understood, but the case of higher dimensions still presents many open problems and conjectures. The chapters in the second part of the book treat questions at the interface of harmonic analysis and number theory, including applications of the Poisson summation formula to crystallography and arithmetic, estimates of the Minkowski dimension of Riemann graphs, random lattice point problems, and the role of Weyl sums in atomic energy oscillations. With a focus on rigorous research insights for graduate students and researchers in mathematics, this book provides a comprehensive journey through the hidden landscapes of harmonic analysis.