Hooks generate the representation ring of the symmetric group
نویسندگان
چکیده
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Representation Theory of the Symmetric Group
Remark 1.2. The definition of an FG-module is more technical than the definition of a representation of G, but, as the exercise shows, the two notions are equivalent. Module can be more convenient to work with, because there is less notation, and we can use results from ring theory without any translation. The language of representations is preferable if we want to have an explicit map ρ : G→ G...
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The paper contains proofs of the following results. For all sufficiently large odd integers n, there exists a set of 2n−1 permutations that pairwise generate the symmetric group Sn. There is no set of 2n−1 + 1 permutations having this property. For all sufficiently large integers n with n≡ 2 mod 4, there exists a set of 2n−2 even permutations that pairwise generate the alternating group An. The...
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ژورنال
عنوان ژورنال: Expositiones Mathematicae
سال: 2012
ISSN: 0723-0869
DOI: 10.1016/j.exmath.2012.03.005