On Stanley’s inequalities for character multiplicities

Mnukhin, V. B. and Siemons, Johannes (2011) On Stanley’s inequalities for character multiplicities. Archiv der Mathematik, 97 (6). pp. 513-521. ISSN 0003-889X

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Abstract

Let G be a group of automorphisms of a ranked poset Q and let N k denote the number of orbits on the elements of rank k in Q . What can be said about the N k for standard posets, such as finite projective spaces or the Boolean lattice? We discuss the connection of this question to the representation theory of the group, and in particular to the inequalities of Livingstone-Wagner and Stanley. We show that these are special cases of more general inequalities which depend on the prime divisors of the group order. The new inequalities often yield stronger bounds depending on the order of the group.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics
Depositing User:	Users 2731 not found.
Date Deposited:	11 Jan 2012 14:24
Last Modified:	24 Sep 2024 09:05
URI:	https://ueaeprints.uea.ac.uk/id/eprint/36101
DOI:	10.1007/s00013-011-0321-7

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