2024/11/22 by Cirpons, Reinis, East, James, Mitchell, James D.
#Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2411.14693
We obtain formulae for the minimum transformation degrees of the most well-studied families of finite diagram monoids, including the partition, Brauer, Temperley--Lieb and Motzkin monoids. For example, the partition monoid Pn has degree 1 + \fracB(n+2)-B(n+1)+B(n)2 for n≥2, where these are Bell numbers. The proofs involve constructing explicit faithful representations of the minimum degree, many of which can be realised as (partial) actions on projections.