Hall-Littlewood polynomials and fixed point enumeration

Details Hall-Littlewood polynomials and fixed point enumeration Hall-Littlewood polynomials and fixed point enumeration

2010-05-14

arxiv.org/abs/1005.2566v1

Discrete Math., vol. 310, issue 4, (2010), 869-876

Mathematics

Combinatorics

Scientific paper

We resolve affirmatively some conjectures of Reiner, Stanton, and White \cite{ReinerComm} regarding enumeration of transportation matrices which are invariant under certain cyclic row and column rotations. Our results are phrased in terms of the bicyclic sieving phenomenon introduced by Barcelo, Reiner, and Stanton \cite{BRSBiD}. The proofs of our results use various tools from symmetric function theory such as the Stanton-White rim hook correspondence \cite{SW} and results concerning the specialization of Hall-Littlewood polynomials due to Lascoux, Leclerc, and Thibon \cite{LLTUnity} \cite{LLTRibbon}.

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