Identities and bases in the sylvester and Baxter monoids

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