University of Birmingham > Talks@bham > Mathematics Colloquium > Containers in Combinatorics

Containers in Combinatorics

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A hypergraph with vertex set, say, {1,2,...,n} is a collection of subsets of the vertex set of some fixed size – these subsets are called edges. For example, the subsets might be all triples that form an arithmetic progression. An independent set in the hypergraph is a subset of the vertices that contain no edge – in the example, it would be a set of integers containing no 3-AP. It has recently been discovered that the independent sets in any hypergraph must be structured in some way: they are all contained within one of a small collection of “independent-like” subsets. We shall discuss this discovery and its applications.

This talk is part of the Mathematics Colloquium series.

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