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Theoretical analysis uncovers finite basis properties in Coxeter group biHecke monoids, highlighting distinct equational behavior between monoid types.
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.
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Gao et al. (2026) studied this question.
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