Outside nested decompositions of skew diagrams and Schur function determinants
Outside nested decompositions of skew diagrams and Schur function determinants
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偏斜图和 Schur 函数行列式的外部嵌套分解
DOI：
10.1016/j.ejc.2017.08.007
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
E. Y. Jin
中科院分区：
文献类型：
--
作者：
E. Y. Jin
我们描述了加厚的条带，并介绍了任何斜形状λ scin μ的外部嵌套分解。对于偏斜形状λ scin μ的任何这样的分解Φ=（Θ 1，Θ 2，.，Θ g），其中Θ i是对于每个i的加厚带，令r是包含在Φ的任何两个不同加厚带中的盒的数量。然后建立了以加厚条的Schur函数为元素的函数p1 r（X）s λ scin μ（X）的行列式公式，其中s λ scin μ（X）是斜形状的Schur函数λ scin μ，p1 r（X）是以分划（1 r）为指标的幂和对称函数.这推广了Hamel和Goulden关于斜形状λ scin μ的外分解的定理，并且我们的扩展是由m-条tableaux的计数所激发的，这是Baryshnikov和Romik通过扩展Elkies的转移算子方法首先计数的。
We describe the thickened strips and introduce the outside nested decompositions of any skew shape λ∕ μ. For any such decomposition Φ=(Θ 1, Θ 2,…, Θ g) of the skew shape λ∕ μ where Θ i is a thickened strip for every i, let r be the number of boxes that are contained in any two distinct thickened strips of Φ. Then we establish a determinantal formula of the function p 1 r (X) s λ∕ μ (X) with the Schur functions of thickened strips as entries, where s λ∕ μ (X) is the Schur function of the skew shape λ∕ μ and p 1 r (X) is the power sum symmetric function indexed by the partition (1 r). This generalizes Hamel and Goulden’s theorem on the outside decompositions of the skew shape λ∕ μ and our extension is motivated by the enumeration of m-strip tableaux, which was first counted by Baryshnikov and Romik via extending the transfer operator approach due to Elkies.