Seminar on Discrete Mathematics: Symmetric functions and alternating sign matrices

报告人：Ilse Fischer（奥地利维也纳大学）

时  间：2026年6月3日15:00

地  点：Zoom会议: 668 1611 9699（密码: 412346）

内容摘要:

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. 

个人简介：

Ilse Fischer，奥地利维也纳大学数学学院副院长，教授，主要研究领域是代数组合学。2000年在奥地利维也纳大学获得博士学位，曾获得美国数学协会David P. Robbins奖和奥地利国家基金委START奖，目前已经在众多数学权威期刊上《Adv. Math.》，《Forum Math. Sigma》,《Int. Math. Res. Not.》，《J. Comb. Theory Ser. A》,《Trans. Am. Math. Soc.》发表多篇文章。

联系人：靳宇