2000 character limit reached
The lattice of submonoids of the uniform block permutations containing the symmetric group (2405.09710v1)
Published 15 May 2024 in math.CO and math.GR
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 $\mathscr{J}$-classes of the uniform block permutation monoid are sums of squares of dimensions of irreducible modules of the monoid algebra.
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