Mathematics & Statistics Colloquium - Eoghan McDowell, Royal Holloway, University of London

Wednesday, November 18, 2020 - 15:00
MS Teams

Title: Counting paths in lattices to obtain symmetric polynomial identities

Speaker: Eoghan McDowell, Royal Holloway, University of London

The talks will be held virtually this semester via Microsoft Teams. Link to join the meeting is given below.  All are welcome.
TO JOIN CLICK: Join Microsoft Teams Meeting

The Lindström--Gessel--Viennot lemma states that the number of non-intersecting tuples of paths in a given lattice is equal to the determinant of a certain matrix. In this talk I will explain the elegant combinatorial argument behind this result, and use it to obtain a new symmetric polynomial identity. This identity generalises both the binomial determinant duality of theorem of Gessel and Viennot and the symmetric function duality theorem of Aitken. I will also mention some motivation from the problem of plethysm in the representation theory of the general linear group.

Image Source -