2013/08/16 by Matthew Fayers, Fayers, Matthew
Mathematics · #05A17 #05E10 #05E18 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A17 #msc:05E10 #msc:05E18
paper · pdf · doi:10.48550/arxiv.1308.3669
openalex publication_date 2013/08/16 · arxiv created 2014/05/12 · arxiv updated 2014/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose s and t are coprime natural numbers. A theorem of Olsson says that the t-core of an s-core partition is again an s-core. We generalise this theorem, showing that the s-weight of the t-core of a partition λ is at most the s-weight of λ. Then we consider the set \mathcal Cs:t of partitions for which equality holds, which we call [s:t]-cores; this set has interesting structure, and we expect that it will be the subject of future study. We show that the set of [s:t]-cores is a union of finitely many orbits for an action of a Coxeter group of type As-1× At-1 on the set of partitions. We also consider the problem of constructing an [s:t]-core with specified s-core and t-core.