论文标题
非共同逆Kostka矩阵的组合解释
A combinatorial interpretation of the noncommutative inverse Kostka matrix
论文作者
论文摘要
我们提供了一个组合公式，用于扩展完整的非共同对称函数到完全同质的非共同对称函数中。为此，我们介绍了Ferrers图的概括，我们称之为GBPR图。我们定义了隧道钩子，它的作用类似于eğecioğlu-remmel公式中出现的特殊边缘钩子的钩子，用于对称逆Kostka矩阵。我们将此解释扩展到偏斜的形状，并完全概括以定义由整数序列偏向整数序列所索引的完美函数。最后，作为我们组合公式的应用，我们将坎贝尔的结果扩展到完美的功能的色带分解上，以至于更大的形状。
We provide a combinatorial formula for the expansion of immaculate noncommutative symmetric functions into complete homogeneous noncommutative symmetric functions. To do this, we introduce generalizations of Ferrers diagrams which we call GBPR diagrams. We define tunnel hooks, which play a role similar to that of the special rim hooks appearing in the Eğecioğlu-Remmel formula for the symmetric inverse Kostka matrix. We extend this interpretation to skew shapes and fully generalize to define immaculate functions indexed by integer sequences skewed by integer sequences. Finally, as an application of our combinatorial formula, we extend Campbell's results on ribbon decompositions of immaculate functions to a larger class of shapes.
