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arXiv · 2503.06329

The Layered Catalan Monoids: Structure and Determinants

M. H. Shahzamanian
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Abstract

In this paper, we introduce and study a class of monoids, called Layered Catalan Monoids (\( {LC}_n \)), which satisfy the structural conditions for $\ll$-smoothness as defined in~\cite{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 \(1 \leq n \leq 7\) but vanishes for \(n \geq 8\).

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M. H. Shahzamanian. 2025-03-08. The Layered Catalan Monoids: Structure and Determinants. https://arxiv.org/abs/2503.06329

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