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Representations and identities of Baxter monoids with involution.
- Source :
-
Semigroup Forum . Oct2023, Vol. 107 Issue 2, p424-458. 35p. - Publication Year :
- 2023
-
Abstract
- Let (baxt n , ♯) be the Baxter monoid of finite rank n with Schützenberger's involution ♯ . In this paper, it is shown that (baxt n , ♯) admits a faithful representation by an involution monoid of upper triangular matrices over any semiring from a large class including the tropical semiring under the skew transposition. Then a transparent combinatorial characterization of the word identities satisfied by (baxt n , ♯) is given. Further, it is proved that (baxt n , ♯) is finitely based if and only if n ≠ 3 , and shown that the identity checking problem for (baxt n , ♯) is decidable in polynomial time. [ABSTRACT FROM AUTHOR]
- Subjects :
- *POLYNOMIAL time algorithms
*MONOIDS
Subjects
Details
- Language :
- English
- ISSN :
- 00371912
- Volume :
- 107
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Semigroup Forum
- Publication Type :
- Academic Journal
- Accession number :
- 173603097
- Full Text :
- https://doi.org/10.1007/s00233-023-10388-5