The finite basis problem for biHecke monoids of a finite Coxeter group

Let [Formula: see text] and [Formula: see text] be the biHecke monoids associated with Coxeter groups of types [Formula: see text] and [Formula: see text], respectively. In this paper, we explore the finite basis problems for biHecke monoids [Formula: see text] and [Formula: see text] and their Borel submonoids [Formula: see text] and [Formula: see text]. It is shown that [Formula: see text] and [Formula: see text] are inherently non-finitely based for all [Formula: see text], [Formula: see text] is hereditarily finitely based and [Formula: see text] is non-finitely based.