عنوان

Algorithmic and Symbolic Combinatorics

شابک

9783030670795

شماره

E1072

زبان متن نوشتاري يا گفتاري و مانند آن

انگلیسی

عنوان اصلي

Algorithmic and Symbolic Combinatorics

نام عام مواد

[Electronic book]

ساير اطلاعات عنواني

An Invitation to Analytic Combinatorics in Several Variables :

نام نخستين پديدآور

/ Stephen Melczer

محل نشرو پخش و غیره

Cham

نام ناشر، پخش کننده و غيره

: Springer International Publishing

تاریخ نشرو بخش و غیره

, 2021

نام خاص و کميت اثر

1 online ressource (XVIII, 418 p. 45 illus., 36 illus. in color)

عنوان فروست

Texts and Monographs in Symbolic Computation Series

متن يادداشت

Intro -- Foreword -- Preface -- Contents -- List of Symbols -- Chapter 1 Introduction -- 1.1 Algorithmic Combinatorics -- 1.1.1 Analytic Methods for Asymptotics -- 1.1.2 Lattice Path Enumeration -- 1.2 Diagonals and Analytic Combinatorics in Several Variables -- 1.2.1 The Basics of Analytic Combinatorics in Several Variables -- 1.2.2 A History of Analytic Combinatorics in Several Variables -- 1.3 Organization -- References -- Part I Background and Motivation -- Chapter 2 Generating Functions and Analytic Combinatorics -- 2.1 Analytic Combinatorics in One Variable2.1.1 AWorked Example: Alternating Permutations -- 2.1.2 The Principles of Analytic Combinatorics -- 2.1.3 The Practice of Analytic Combinatorics -- 2.2 Rational Power Series -- 2.3 Algebraic Power Series -- 2.4 D-Finite Power Series -- 2.4.1 An Open Connection Problem -- 2.5 D-Algebraic Power Series -- Appendix on Complex Analysis -- Problems -- References -- Chapter 3 Multivariate Series and Diagonals -- 3.1 Complex Analysis in Several Variables -- 3.1.1 Singular Sets of Multivariate Functions -- 3.1.2 Domains of Convergence for Multivariate Power Series -- 3.2 Diagonals3.2.1 Properties of Diagonals -- 3.2.2 Representing Series Using Diagonals -- 3.3 Multivariate Laurent Expansions and Other Series Operators -- 3.3.1 Convergent Laurent Series and Amoebas -- 3.3.2 Diagonals and Non-Negative Extractions of Laurent Series -- 3.4 Sources of Rational Diagonals -- 3.4.1 Binomial Sums -- 3.4.2 Irrational Tilings -- 3.4.3 Period Integrals -- 3.4.4 Kronecker Coefficients -- 3.4.5 Positivity Results and Special Functions -- 3.4.6 The Ising Model and Algebraic Diagonals -- 3.4.7 Other Sources of Examples -- Problems -- ReferencesChapter 4 Lattice Path Enumeration, the Kernel Method, and Diagonals -- 4.1 Walks in Cones and The Kernel Method -- 4.1.1 Unrestricted Walks -- 4.1.2 A Deeper Kernel Analysis: One-Dimensional Excursions -- 4.1.3 Walks in a Half-Space -- 4.1.4 Walks in the Quarter-plane -- 4.1.5 OrthantWalks Whose Step Sets Have Symmetries -- 4.2 Historical Perspective -- 4.2.1 The Kernel Method -- 4.2.2 Recent History of Lattice Paths in Orthants -- Problems -- References -- Part II Smooth ACSV and Applications -- Chapter 5 The Theory of ACSV for Smooth Points -- 5.1 Central Binomial Coefficient Asymptotics5.1.1 Asymptotics in General Directions -- 5.1.2 Asymptotics of Laurent Coefficients -- 5.2 The Theory of Smooth ACSV -- 5.3 The Practice of Smooth ACSV -- 5.3.1 Existence of Minimal Critical Points -- 5.3.2 Dealing with Minimal Points that are not Critical -- 5.3.3 Perturbations of Direction and a Central Limit Theorem -- 5.3.4 Genericity of Assumptions -- Problems -- References -- Chapter 6 Application: Lattice Walks and Smooth ACSV -- 6.1 Asymptotics of Highly Symmetric Orthant Walks -- 6.1.1 Asymptotics for All Walks in an Orthant -- 6.1.2 Asymptotics for Boundary Returns

بدون عنوان

0

عنصر شناسه ای

Logic, Symbolic and mathematical

عنصر شناسه ای

Discrete mathematics

عنصر شناسه ای

Algorithms

داده رابط بین فیلدها

a05

شماره رده

عنصر شناسه اي

Melczer, Stephen

کشور

ایران

سازمان

032

تاريخ عمليات

20211229

تاريخ و ساعت مذاکره و دسترسي

UT_SCI_BL_DB_1000008_0001.pdf

فرمت انتشار

e

نوع ماده

BL

کد کاربرگه

278840

پیشوند ISBD اعمال شده است

1

تكميل شده

Y