1. Representations and identities of Baxter monoids with involution.
- Author
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Han, Bin Bin, Zhang, Wen Ting, Luo, Yan Feng, and Zhao, Jin Xing
- Subjects
POLYNOMIAL time algorithms ,MONOIDS - 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]
- Published
- 2023
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