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CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Thursday, October 26, 2017 - 3:00pm

George Wang



University of Pennsylvania


Quasi-Yamanouchi tableaux are a subset of semistandard Young tableaux that are also a refinement on standard Young tableaux, and they can be used to improve the fundamental quasisymmetric expansion of Schur polynomials. We prove a product formula for enumerating quasi-Yamanouchi tableaux of Durfee size two and provide strong evidence that no product formula exists in general for other shapes. Along the way, we also prove some nice properties of their distribution and symmetry. Finally, we present two new, seemingly unrelated conjectures on the Schur expansion of Jack polynomials and find that quasi-Yamanouchi tableaux make a surprising appearance.