Cyclic Sieving, Necklaces, and Branching Rules Related to Thrall's Problem
Keyword(s):
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 Kraśkiewicz-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.
2004 ◽
Vol 108
(1)
◽
pp. 17-50
◽
2019 ◽
Vol 15
(09)
◽
pp. 1919-1968
◽
2011 ◽
Vol DMTCS Proceedings vol. AO,...
(Proceedings)
◽
Keyword(s):
2010 ◽
Vol DMTCS Proceedings vol. AN,...
(Proceedings)
◽
2011 ◽
Vol DMTCS Proceedings vol. AO,...
(Proceedings)
◽
Keyword(s):
2016 ◽
Vol 20
(3)
◽
pp. 609-621
◽