Identities in Plactic, Hypoplactic, Sylvester, Baxter, and Related Monoids

Identities in Plactic, Hypoplactic, Sylvester, Baxter, and Related Monoids

 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...

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Veröffentlicht in:The Electronic journal of combinatorics 2018-08, Vol.25 (3)
Hauptverfasser: Cain, Alan J., Malheiro, António
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description  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.
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title Identities in Plactic, Hypoplactic, Sylvester, Baxter, and Related Monoids
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