Statistical enumeration of groups by double cosets
Statistical enumeration of groups by double cosets
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DOI：
10.1016/j.jalgebra.2021.05.010
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发表时间：
2021-02
影响因子：
0.9
通讯作者：
P. Diaconis;Mackenzie Simper
中科院分区：
文献类型：
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作者：
P. Diaconis;Mackenzie Simper
设H和K是有限群G的子群.随机一致选取g∈ G。研究了双陪集上的诱导分布。给出了三个例子：1）H= K= G Ln（Fq）中的Borel子群.这导致了新的定理马洛措施的排列和新的见解到LU矩阵分解。2)S2 n内部超八面体群的二重陪集，从而引出了Ewens抽样公式在数学遗传学中的新应用。3)最后，如果H和K是S n的抛物子群，则双陪集是统计学家在过去100年中研究的“列联表”。
Let H and K be subgroups of a finite group G. Pick g∈ G uniformly at random. We study the distribution induced on double cosets. Three examples are treated in detail: 1) H= K= the Borel subgroup in G L n (F q). This leads to new theorems for Mallows measure on permutations and new insights into the LU matrix factorization. 2) The double cosets of the hyperoctahedral group inside S 2 n, which leads to new applications of the Ewens's sampling formula of mathematical genetics. 3) Finally, if H and K are parabolic subgroups of S n, the double cosets are ‘contingency tables’, studied by statisticians for the past 100 years.