You are here: Seminars > 2025 > June 4th
University of Cambridge
Time: 16:00-17:00 (GMT+8), Wednesday June 4th, 2025
Location: Zoom
Abstract:
In 1970s, Baranyai showed that every \(k\)-uniform complete hypergraph of \(n\) such that \(k \mid n\) can be decomposed into perfect matchings, thus confirming a long-standing conjectured generalization of Kirkman's schoolgirl problem. At the end of his paper, he conjectured an even stronger statement, the "wreath conjecture". To this day, it is open. Katona wrote about the wreath conjecture: "This conjecture [...] seems to be too algebraic. One does not expect to solve it without algebra. (Unless it is not true.)”
In this talk, we look at an algebraic approach to the conjecture, analyzing a matrix encoding the problem. We discuss the properties of the matrix, as well as how other decomposition problems can be approached in this way.
The talk is based on joint work with Pavel Turek.
Host: 陈俊彦 Junyan Chen