An iterative formula for the Kostka–Foulkes polynomials is given using the vertex operator realization of the Hall–Littlewood polynomials. The operational formula can handle large Kostka–Foulkes polynomials, and a stability property for the Kostka–Foulkes polynomials is shown. We also use our algorithm to give a formula of \(K_{\lambda \mu }(t)\) for \(\mu \) being hook-shaped.

中文翻译：

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Kostka-Foulkes多项式的迭代公式

使用Hall–Littlewood多项式的顶点算子实现，给出了Kostka–Foulkes多项式的迭代公式。该运算公式可以处理大的Kostka-Foulkes多项式，并显示了Kostka-Foulkes多项式的稳定性。我们还使用我们的算法，得到的式\（K _ {\拉姆达\亩}（T）\）为\（\亩\）被钩形。