Cyclic sieving, necklaces, and branching rules related to Thrall's\n problem

2018/08/18 by Connor Ahlbach, Ahlbach, Connor, Joshua P. Swanson +1 · 1 citation
Mathematics · #05E10 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1808.06043

openalex publication_date 2018/08/18 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28

Abstract

We show that the cyclic sieving phenomenon of Reiner--Stanton--White together\nwith necklace generating functions arising from work of Klyachko offer a\nremarkably unified, direct, and largely bijective approach to a series of\nresults due to Kraskiewicz--Weyman, Stembridge, and Schocker related to the\nso-called higher Lie modules and branching rules for inclusions C_a wr S_b\n hookrightarrow S_ab . Extending the approach gives monomial expansions for\ncertain graded Frobenius series arising from a generalization of Thrall's\nproblem.\n

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• Asymptotics of higher Lie characters

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