Multi-atoms and Monotonicity of Generalized Kostka Polynomials
Multi-atoms and Monotonicity of Generalized Kostka Polynomials
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广义Kostka多项式的多原子性和单调性
DOI：
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发表时间：
1998
期刊：
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通讯作者：
M. Shimozono
中科院分区：
文献类型：
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作者：
M. Shimozono
在几何学中有一类自然产生的庞加莱多项式。它们满足单调性，并允许用分次偏序集的形式进行组合描述，其元素称为Littlewood？Richardson表。本文的目的是通过证明这些分次偏序集的嵌入性，给出单调性的一个组合解释。特别地，这些偏序集嵌入到LasCoux和Schutzenberger的周期偏序集中，从而解释了Kostka？Foulkes多项式的单调性。刻画了嵌入到周期偏序集中的映象，给出了Poincare多项式的另一种组合刻画，即作者和J.Weyman定义的可分解图。
There is a certain family of Poincare polynomials that arise naturally in geometry. They satisfy a monotonicity property and admit a combinatorial description in terms of a graded poset whose elements are called Littlewood?Richardson tableaux. The purpose of this article is to give a combinatorial explanation of the monotonicity by exhibiting embeddings of these graded posets. In particular, these posets embed into the cyclage poset of Lascoux and Schutzenberger, which was introduced to explain the monotonicity of the Kostka?Foulkes polynomials. The image of the embedding into the cyclage poset is characterized, giving another combinatorial description of the Poincare polynomials in terms of the catabolizable tableaux defined by the author and J. Weyman.