Title: Counting paths in lattices to obtain symmetric polynomial identities
Speaker: Eoghan McDowell, Royal Holloway, University of London
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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.
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