We show that any polynomial tau-function of the s-component KP and the BKP hierarchies can be interpreted as a zero-mode of an appropriate combinatorial generating function. As an application, we obtain explicit formulas for all polynomial tau-functions of these hierarchies in terms of Schur polynomials and Q-Schur polynomials, respectively. We also obtain formulas for polynomial tau-functions of the reductions of the s-component KP hierarchy associated with partitions in s parts.

中文翻译：

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KP，BKP和thes组件KP层次结构的多项式tau函数

我们表明，s成分KP和BKP层次结构的任何多项式tau函数都可以解释为适当组合生成函数的零模式。作为应用，我们分别根据Schur多项式和Q -Schur多项式获得了这些层次结构的所有多项式tau函数的显式。我们还获得了与s部分中的分区相关联的s成分KP层次结构约简的多项式tau函数的公式。