Set families and Foulkes modules
Set families and Foulkes modules
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设置系列和福克斯模块
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
M. Wildon
中科院分区：
文献类型：
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作者：
Rowena Paget;M. Wildon
我们构造了一类新的对称群的从Specht模到Foulkes模的同态。这些同态被用来给一个组合的最小分区（在优势顺序）的标签出现的不可约字符作为和的字符的福克斯模块的描述。同态是用自然数的子集的某些族定义的。这些家庭是独立的利益，我们证明了一些关于他们的组合结果。
We construct a new family of homomorphisms from Specht modules into Foulkes modules for the symmetric group. These homomorphisms are used to give a combinatorial description of the minimal partitions (in the dominance order) which label the irreducible characters appearing as summands of the characters of Foulkes modules. The homomorphisms are defined using certain families of subsets of the natural numbers. These families are of independent interest; we prove a number of combinatorial results concerning them.