Symmetric group character degrees and hook numbers

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15 Citations (Scopus)


In this article we prove the following result: for any two natural numbers k and ℓ, and for all sufficiently large symmetric groups Sn, there are k disjoint sets of ℓ irreducible characters of Sn, such that each set consists of characters with the same degree, and distinct sets have different degrees. In particular, this resolves a conjecture most recently made by Moretó in [5]. The methods employed here are based upon the duality between irreducible characters of the symmetric groups and the partitions to which they correspond. Consequently, the paper is combinatorial in nature.
Original languageEnglish
Pages (from-to)26-50
Number of pages25
JournalLondon Mathematical Society. Proceedings
Issue number1
Early online date11 Aug 2007
Publication statusPublished - Jan 2008


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