A new algebraic approach to the wreath conjecture

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• Jan Petr (Cambridge)
• Thursday 13 February 2025, 14:30-15:30
• MR12.

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In 1970s, Baranyai proved that the hyperedges of the k-uniform complete hypergraph on n vertices can be decomposed into perfect matchings whenever k divides n. In the same paper, he posed a more general conjecture. Katona, who later rephrased this conjecture as decomposing [n]^(k) into so-called wreaths, wrote “Baranyai’s brilliant idea was to use matrices and flows in networks. This conjecture, however, seems to be too algebraic. One does not expect to solve it without algebra. (Unless it is not true.)”. In this talk, we will discuss a new algebraic approach to the wreath conjecture, defining a matrix encoding the problem and studying its properties. (based on joint work with Pavel Turek)

This talk is part of the Combinatorics Seminar series.

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