The Layered Catalan Monoids: Structure and Determinants
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912265773514752 |
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| author | Shahzamanian, M. H. |
| author_facet | Shahzamanian, M. H. |
| contents | 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 \(n \geq 8\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Layered Catalan Monoids: Structure and Determinants Shahzamanian, M. H. Group Theory Representation Theory 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 \(n \geq 8\). |
| title | The Layered Catalan Monoids: Structure and Determinants |
| topic | Group Theory Representation Theory |
| url | https://arxiv.org/abs/2503.06329 |