The lattice of submonoids of the uniform block permutations containing the symmetric group
Skip to main content
eScholarship
Open Access Publications from the University of California

UC Davis

UC Davis Previously Published Works bannerUC Davis

The lattice of submonoids of the uniform block permutations containing the symmetric group

Published Web Location

https://doi.org/10.1007/s00233-025-10505-6
No data is associated with this publication.
Creative Commons 'BY' version 4.0 license
Abstract

Abstract: We study the lattice of submonoids of the uniform block permutation monoid containing the symmetric group (which is its group of units). We prove that this lattice is distributive under union and intersection by relating the submonoids containing the symmetric group to downsets in a new partial order on integer partitions. Furthermore, we show that the sizes of the $$\mathscr {J}$$ J -classes of the uniform block permutation monoid are sums of squares of dimensions of irreducible modules of the monoid algebra.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Item not freely available? Link broken?
Report a problem accessing this item