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Identities and bases in the sylvester and Baxter monoids.

Authors :
Cain, Alan J.
Malheiro, António
Ribeiro, Duarte
Source :
Journal of Algebraic Combinatorics; Dec2023, Vol. 58 Issue 4, p933-966, 34p
Publication Year :
2023

Abstract

This paper presents new results on the identities satisfied by the sylvester and Baxter monoids. We show how to embed these monoids, of any rank strictly greater than 2, into a direct product of copies of the corresponding monoid of rank 2. This confirms that all monoids of the same family, of rank greater than or equal to 2, satisfy exactly the same identities. We then give a complete characterization of those identities, and prove that the varieties generated by the sylvester and the Baxter monoids have finite axiomatic rank, by giving a finite basis for them. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
09259899
Volume :
58
Issue :
4
Database :
Complementary Index
Journal :
Journal of Algebraic Combinatorics
Publication Type :
Academic Journal
Accession number :
173653088
Full Text :
https://doi.org/10.1007/s10801-022-01202-6