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Asymptotic enumeration of discrete structures: what, how and why

Introductory Workshop: Probability and Statistics of Discrete Structures January 27, 2025 - January 31, 2025

January 30, 2025 (09:30 AM PST - 10:30 AM PST)
Speaker(s): Catherine Greenhill (UNSW Sydney)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Asymptotic enumeration of discrete structures: what, how and why

Abstract

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Asymptotic enumeration involves finding an approximate formula for the size of a combinatorial set, with a relative error that gets smaller as the size of the set grows. For example, we might be interested in the number of hypergraphs with a given number of vertices and satisfying some other nice properties, and how this number behaves as the number of vertices tends to infinity. I will describe some methods for obtaining asymptotic enumeration formulae and some applications to the analysis of random graphs and hypergraphs.

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Asymptotic enumeration of discrete structures: what, how and why

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