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 generalize to the general case and lead to a proof of the whole conjecture.

中文翻译：

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辛 Kostka-Foulkes 多项式的正组合公式 I：行

我们证明了 Lecouvey 的猜想，它在任意权重的行的情况下为辛 Kostka-Foulkes 多项式提出了一个封闭的正组合公式。为了证明这一点，我们将描述猜想的循环算法转换为一个不同的、更方便的组合模型，没有局部约束。特别是，我们表明我们的模型受类型 A 中的情况控制。我们希望我们的方法可以推广到一般情况并导致整个猜想的证明。