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9 papers · 1 filter
Free left and right adequate semigroups
Mark Kambites
Recent research of the author has given an explicit geometric description of free (two-sided) adequate semigroups and monoids, as sets of labelled directed trees under a natural co…
Free adequate semigroups
Mark Kambites
We give an explicit description of the free objects in the quasivariety of adequate semigroups, as sets of labelled directed trees under a natural combinatorial multiplication. The…
On generic properties of finitely presented monoids and semigroups
Mark Kambites
We study the generic properties of finitely presented monoids and semigroups. We show that for positive integers a > 1, k and m, the generic a-generator k-relation monoid and semig…
Small overlap monoids II: automatic structures and normal forms
Mark Kambites
We show that any finite monoid or semigroup presentation satisfying the small overlap condition C(4) has word problem which is a deterministic rational relation. It follows that th…
Graph products of right cancellative monoids
John Fountain, Mark Kambites
Our first main result shows that a graph product of right cancellative monoids is itself right cancellative. If each of the component monoids satisfies the condition that the inter…
Small overlap monoids: the word problem
Mark Kambites
We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods,…