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On a Conjecture of Foulkes

✍ Scribed by Suzie C. Dent; Johannes Siemons

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 172 KB
Volume: 226
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8169

No coin nor oath required. For personal study only.

✦ Synopsis

Suppose that ⍀ s 1, 2, . . . , ab for some non-negative integers a and b. Denote Ž . by P a, b the set of unordered partitions of ⍀ into a parts of cardinality b. In this Ž . paper we study the decomposition of the permutation module C P a, b where C is Ž . the field of complex numbers. In particular, we show that C P 3, b is isomorphic to Ž . a submodule of C P b, 3 for b G 3. This settles the next unproven case of a conjecture of Foulkes.

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