Geodesic
Identities in plactic, hypoplactic, sylvester, Baxter, and related monoids
Alan J. Cain1 ; António Malheiro2
1Centro de Matemática e Aplicações Faculdade de Ciências e Tecnologia Universidade Nova de Lisboa 2829–516 Caparica, Portugal
2Departamento de Matemática and Centro de Matemática e Aplicações Faculdade de Ciências e Tecnologia Universidade Nova de Lisboa 2829–516 Caparica, Portugal
The electronic journal of combinatorics, Tome 25 (2018) no. 3
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This paper considers whether non-trivial identities are satisfied by certain `plactic-like' monoids that, like the plactic monoid, are closely connected to combinatorics. New results show that the hypoplactic, sylvester, Baxter, stalactic, and taiga monoids satisfy identities, and indeed give shortest identities satisfied by these monoids. The existing state of knowledge is discussed for the plactic monoid and left and right patience sorting monoids.
DOI : 10.37236/6873
Classification : 20M05
Mots-clés : plactic-like monoids

Alan J. Cain  1   ; António Malheiro  2

1 Centro de Matemática e Aplicações Faculdade de Ciências e Tecnologia Universidade Nova de Lisboa 2829–516 Caparica, Portugal
2 Departamento de Matemática and Centro de Matemática e Aplicações Faculdade de Ciências e Tecnologia Universidade Nova de Lisboa 2829–516 Caparica, Portugal 
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     author = {Alan J. Cain and Ant\'onio Malheiro},
     title = {Identities in plactic, hypoplactic, sylvester, {Baxter,} and related monoids},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {3},
     doi = {10.37236/6873},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/6873/}
}
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Alan J. Cain; António Malheiro. Identities in plactic, hypoplactic, sylvester, Baxter, and related monoids. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/6873

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