Enumerative combinatorics

Enumerative combinatorics

Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed. Two examples of this type of problem are counting combinations and counting permutations. More generally, given an infinite collection of finite sets Si indexed by the natural numbers, enumerative combinatorics seeks to describe a counting function which counts the number of objects in Sn for each n. Although counting the number of elements in a set is a rather broad mathematical problem, many of the problems that arise in applications have a relatively simple combinatorial description. The twelvefold way provides a unified framework for counting permutations, combinations and partitions. The simplest such functions are closed formulas, which can be expressed as a composition of elementary functions such as factorials, powers, and so on. For instance, as shown below, the number of different possible orderings of a deck of n cards is f(n) = n!. The problem of finding a closed formula is known as algebraic enumeration, and frequently involves deriving a recurrence relation or generating function and using this to arrive at the desired closed form. Often, a complicated closed formula yields little insight into the behavior of the counting function as the number of counted objects grows. In these cases, a simple asymptotic approximation may be preferable. A function is an asymptotic approximation to if as . In this case, we write (Wikipedia).

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Christian Krattenthaler - Determinants and Pfaffians in Enumerative Combinatorics (2011)

Slides for this talk: http://www.mat.univie.ac.at/~kratt/vortrag/combdet.pdf Abstract: In this talk I shall explain why many enumerative combinatorialists are fascinated by determinants — obviously from a strongly biased personal perspective. The particular sources where determinants ari

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Cyril Banderier - Enumeration and Generation of Young Tableaux with Walls: the Density Method

We consider a generalization of Young tableaux in which we allow some consecutive pairs of cells with decreasing labels, conveniently visualized by a ”wall” between the corresponding cells. This leads to new classes of recurrences, and to a surprisingly rich zoo of generating functions (al

From playlist Combinatorics and Arithmetic for Physics: special days

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Large deviations for random hives and the spectrum of the sum of two random.. by Hariharan Narayanan

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Peter Varju: Additive combinatorics methods in fractal geometry - lecture 2

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Circular Fence Posets and Associated Polytopes with Unexpected Symmetry by Mohan Ravichandran

PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t

From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)

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Enumerative Combinatorics of Maps - CEB T1 2017 - Bousquet-Mélou - 2/10

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Enumerative Combinatorics of Maps - CEB T1 2017 - Bousquet-Mélou - 1/10

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Enumerative Combinatorics of Maps - CEB T1 2017 - Bousquet-Mélou - 3/10

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Pablo Shmerkin: Additive combinatorics methods in fractal geometry - lecture 1

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Enumerative Combinatorics of Maps - CEB T1 2017 - Bousquet-Mélou - 5/10

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Enumerative Combinatorics of Maps - CEB T1 2017 - Bousquet-Mélou - 8/10

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Philippe Flajolet, founder of Analytic Combinatorics (2012)

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Catalan number | Exponentiation | Coefficient | Algebraic enumeration | Derivative | Permutation | Ronald Graham | Combinatorics | Factorial | Combinatorial species | Burnside's lemma | Sequence | Asymptotic analysis | Tree (graph theory) | Combinatorial game theory | Disjoint union | Binomial theorem | Combinatorial principles | Counting | Binomial coefficient | Natural number | Recurrence relation | Partition of a set | Cycle (graph theory) | Inclusion–exclusion principle | Pólya enumeration theorem | Cartesian product | Combinatorial explosion | Sieve theory | Mathematical problem | Square root | Algebraic combinatorics | Method of distinguished element | Twelvefold way | Binary tree | Generating function | Combination