Cyclic Sieving, Necklaces, and Branching Rules Related to Thrall's Problem

  • Connor Ahlbach
  • Joshua P. Swanson
Keywords: Cyclic sieving, Necklaces, Branching rules, Thrall's problem, Wreath products, Plethysm, Major index

Abstract

We show that the cyclic sieving phenomenon of Reiner-Stanton-White together with necklace generating functions arising from work of Klyachko offer a remarkably unified, direct, and largely bijective approach to a series of results due to Kraƛkiewicz-Weyman, Stembridge, and Schocker related to the so-called higher Lie modules and branching rules for inclusions $ C_a \wr S_b \hookrightarrow S_{ab} $. Extending the approach gives monomial expansions for certain graded Frobenius series arising from a generalization of Thrall's problem.

Published
2018-11-30
Article Number
P4.42