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



Autor: Brendon Rhoades

Fuente: https://arxiv.org/







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