3 papers
math.RA2025
Counting finite semirings
J. Edwards, J. D. Mitchell, P. Ragavan
In this short note we count the finite semirings up to isomorphism, and up to isomorphism or anti-isomorphism for some small values of ; for which we utilise the existing librar…
math.CO2024
Semirigidity and the enumeration of nilpotent semigroups of index three
Igor Dolinka, D. G. FitzGerald, James D. Mitchell
There is strong evidence for the belief that `almost all' finite semigroups, whether we consider multiplication operations on a fixed set or their isomorphism classes, are nilpoten…
math.GR2024
Short presentations for transformation monoids
Thomas Aird, James D. Mitchell, Murray T. Whyte
By the theorems of Cayley and Vagner-Preston, the full transformation monoids and the symmetric inverse monoids play analogous roles in the theory of monoids and inverse monoids, a…