An Invitation to Analytic Combinatorics
نویسنده
چکیده
ANALYTIC COMBINATORICS is primarily a book about combinatorics, that is, the study of finite structures built according to a finite set of rules. Analytic in the title means that we concern ourselves with methods from mathematical analysis, in particular complex and asymptotic analysis. The two fields, combinatorial enumeration and complex analysis, are organized into a coherent set of methods for the first time in this book. Our broad objective is to discover how the continuous may help us to understand the discrete and to quantify its properties.
منابع مشابه
The Order Steps of an Analytic Combinatorics
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. This 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 caref...
متن کاملAnalytic Combinatorics of Chord Diagrams Analytic Combinatorics of Chord Diagrams Combinatoire Analytique Des Diagrammes De Cordes Analytic Combinatorics of Chord Diagrams
In this paper we study the enumeration of diagrams of n chords joining 2n points on a circle in disjoint pairs. We establish limit laws for the following three parameters: number of components, size of the largest component, and number of crossings. We also nd exact formulas for the moments of the distribution of number of components and number of crossings. Key-words: Analytic combinatorics, c...
متن کاملAnalytic combinatorics of connected graphs
We enumerate the connected graphs that contain a linear number of edges with respect to the number of vertices. So far, only first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, i.e. generating function manipulations, we derive the complete asymptotic expansion. keywords. connected graphs, analytic combinatorics, generating functions, asymptotic expan...
متن کاملMappings On Decomposable Combinatorial Structures: Analytic Approach
Combinatorics, Probability & Computing / Volume 11 / Issue 01 / January 2002, pp 61 78 DOI: 10.1017/S0963548301005016, Published online: 14 February 2002 Link to this article: http://journals.cambridge.org/abstract_S0963548301005016 How to cite this article: E. MANSTAVICIUS (2002). Mappings on Decomposable Combinatorial Structures: Analytic Approach. Combinatorics, Probability & Computing, 11, ...
متن کاملAnalytic combinatorics for a certain well-ordered class of iterated exponential terms
The aim of this paper is threefold: firstly, to explain a certain segment of ordinals in terms which are familiar to the analytic combinatorics community, secondly to state a great many of associated problems on resulting count functions and thirdly, to provide some weak asymptotic for the resulting count functions. We employ for simplicity Tauberian methods. The analytic combinatorics communit...
متن کامل