Mathematics Colloquium with Cory Palmer (University of Montana) 10/25

10/19/2023
By Joris Roos

The Department of Mathematics & Statistics invites you to attend a colloquium talk given by Cory Palmer (University of Montana). This is a virtual a talk. Everyone is welcome to attend via Zoom.

Title: A generalization of derangements

Date: Wednesday, Oct 25
Time: 11 a.m. - Noon
Via Zoom

Abstract: A derangement is a permutation with no fixed points (i.e.no element that appears in its original position). The problem of counting derangements was introduced by de Montmort in 1708 and solved by him in 1713. For large n, the number of derangements of an n-element set is approximately n!/e.

The number of derangements of an n-element set can be realized as the number of perfect matchings in a complete bipartite graph K_{n,n} with a perfect matching removed. A related problem is the number of perfect matchings in the complete graph K_{2n} with a perfect matching removed. For large n, this value is approximately (2n-1)!! / sqrt{e}. In this talk we discuss these two parameters and a common generalization.