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- Title
Reductions for vector ( n, m)-presentations of ( n, m)-semigroups.
- Authors
Dimovski, Dončo; Stojmenovska, Irena
- Abstract
We investigate questions from the combinatorial theory of ( n, m)-semigroups and construct reductions for a special class of ( n, m)-presentations of ( n, m)-semigroups, called vector ( n, m)-presentations of ( n, m)-semigroups. A vector ( n, m)-presentation of an ( n, m)-semigroup 〈 B;Δ〉 induces a binary semigroup presentation 〈 B;Λ〉. We show that the existence of a good combinatorial description for the binary semigroup 〈 B;Λ〉 implies the existence of a good combinatorial description for the ( n, m)-semigroup 〈 B;Δ〉. We also show that under some conditions on 〈 B;Λ〉, the obtained good combinatorial description for 〈 B;Δ〉 implies the solvability of the word problem for 〈 B;Δ〉.
- Subjects
VECTORS (Calculus); GROUP presentations (Mathematics); SEMIGROUPS (Algebra); COMBINATORIAL group theory; REWRITING systems (Computer science); WORD problems (Mathematics)
- Publication
Semigroup Forum, 2013, Vol 86, Issue 3, p663
- ISSN
0037-1912
- Publication type
Article
- DOI
10.1007/s00233-012-9452-9