Seminar on Discrete Mathematics: Symmetric functions and alternating sign matrices

Speaker：Ilse Fischer（University of Vienna）

Time：2026-6-3 15:00

Location：Zoom Meeting: 733 6295 7214（Password: 260603）

Abstract:

Alternating sign matrices are notorious for being difficult to enumerate. Even more challenging—if not impossible—has been finding satisfying bijective proofs of many equinumerosity results involving them. After a brief historical overview, we introduce generalizations of Schur polynomials that serve as multivariate generating functions for alternating sign matrices. These generalizations satisfy a Cauchy identity as well as a Littlewood identity that generalize the classical ones. This is exciting because Littlewood-type identities are key in several non-bijective proofs of the aforementioned equinumerosity results. Since the classical Cauchy and Littlewood identities have beautiful bijective proofs via the Robinson–Schensted–Knuth (RSK) correspondence, this raises the question of whether there is an RSK correspondence tailored to alternating sign matrices. 

The talk is based on joint work with Moritz Gangl, Hans Höngesberg and Florian Schreier-Aigner.