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Arities of Permutation Groups: Wreath Products andk-Sets

✍ Scribed by Gregory L. Cherlin; Gary A. Martin; Daniel H. Saracino

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 1023 KB
Volume: 74
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1996.0050

No coin nor oath required. For personal study only.

✦ Synopsis

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 on n letters on the set of k-sets from an n-element set, and we estimate it rather closely for symmetric powers of these actions. In the case k=1 we formulate an explicit combinatorial conjecture which would pin down the values exactly in all cases.

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