Alan J. Cain

activity

20092023

most citedFinite Gröbner--Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids

30 citations · 132 across the 31 of their papers we have counts for

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Showing 2023 · math.GRShow all

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math.GR2023

Commutative nilpotent transformation semigroups

Alan J. Cain, António Malheiro, Tânia Paulista

Cameron, et al. determined the maximum size of a null subsemigroup of the full transformation semigroup $T (X)$ on a finite set $X$ and provided a description of the null…

math.GR2023

Every numerical semigroup arises as an automaton monoid

Tara Macalister Brough, Alan J. Cain, Jan Philipp Wächter

This paper shows how to construct explicitly an automaton that generates an arbitrary numerical semigroup.