The Layered Catalan Monoids: Structure and Determinants
Abstract
In this paper, we introduce and study a class of monoids, called Layered Catalan Monoids (\( LCn \)), which satisfy the structural conditions for -smoothness as defined in~Sha-Det2. These monoids are defined by specific identities inspired by Catalan monoids. We establish their canonical forms and compute their determinant, proving that it is non-zero for \(1 ≤ n ≤ 7\) but vanishes for \(n ≥ 8\).
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