Arities of Permutation Groups: Wreath Products and k-Sets
Arities of Permutation Groups: Wreath Products and k-Sets
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排列群的元数：花环积和 k 集
DOI：
10.1006/jcta.1996.0050
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
D. Saracino
中科院分区：
文献类型：
--
作者：
G. Cherlin;Gary A. Martin;D. Saracino
我们引入了一个称为元数的有限置换群的不变量，它对于模型理论家来说是众所周知的，但尚未从代数的角度进行检验。在很少的情况下，这个不变量是明确已知的。我们分析了花环产品的幂表示中这种不变量的行为。我们精确地计算对称群 onnletters 对来自 nn-element 集合的 k-sets 的作用，并且我们对这些作用的对称幂进行相当接近的估计。在 k=1 的情况下，我们制定了一个明确的组合猜想，它将在所有情况下精确地确定值。
We introduce an invariant of finite permutation groups called the arity which is well known to model theorists but has not been examined from an algebraic point of view. There are few cases in which this invariant is known explicitly. We analyze the behavior of this invariant in power representations of wreath products. We compute it exactly for the action of the symmetric group onnletters on the set ofk-sets from ann-element set, and we estimate it rather closely for symmetric powers of these actions. In the casek=1 we formulate an explicit combinatorial conjecture which would pin down the values exactly in all cases.