Séminaire Lotharingien de Combinatoire, 84B.42 (2020), 12 pp.

Maciej Dołęga, Thomas Gerber and Jacinta Torres

A Positive Combinatorial Formula for Symplectic Kostka-Foulkes Polynomials I: Rows

Abstract. We prove a conjecture of Lecouvey, which proposes a closed, positive combinatorial formula for symplectic Kostka-Foulkes polynomials, in the case of rows of arbitrary weight. To show this, we transform the cyclage algorithm in terms of which the conjecture is described into a different, more convenient combinatorial model, free of local constraints. In particular, we show that our model is governed by the situation in type A. We expect our approach to lead to a proof of the conjecture in the general case.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

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