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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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