Mathematics Colloquia and Seminars

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Description

Let G be a finite cyclic group, and G acts on a finite set S, there is a non-negative integer coefficient polynomial P(x) that encodes the structure information of this action. There are many families of triples that behave very nicely. For example, B. Rhoades showed that if \lambda is a square shape, and S=SYT(\lambda) is the set of standard Young tableaux of shape \lambda; and G is the cyclic group generated by the promotion operator, then P is the generating polynomial of the major index statistics on S (closely related to the q-analogues of hook length formula). Situation like this is called a Cyclic Sieving Phenomenon (Barcelo, Reiner and Stanton, 2007) In this talk, I will discuss our (with Steve Pon) on going investigation on the case \lambda is the stair case shape. We strongly believe that there exits a Cyclic Sieving Phenomenon.