We introduce the monoid of the admissible KF polynomials. These polynomials are invariant under uniform translation of partitions. Moreover, each Kostka–Foulkes polynomial turns out to be a linear combination of admissible KF polynomials with coefficients \(-1\) or 1. Elementary manipulations of triangular matrices provide identities on Kostka–Foulkes polynomials which are not obvious a priori.

中文翻译：

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Kostka-Foulkes多项式的一个对映体

我们介绍了可允许的KF多项式的monoid。这些多项式在分区的均匀转换下是不变的。而且，每个Kostka-Foulkes多项式都是允许的KF多项式与系数\（-1 \）或1的线性组合。对三角形矩阵的基本操作提供了Kostka-Foulkes多项式的先验身份，而后者显然不是先验的。