$t$-Young complexes and squarefree powers of $t$-path ideals
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912716072943616 |
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| author | Navarra, Francesco Qureshi, Ayesha Asloob Veer, Dharm |
| author_facet | Navarra, Francesco Qureshi, Ayesha Asloob Veer, Dharm |
| contents | We introduce a new class of simplicial complexes, called \emph{$t$-Young complexes}, arising from a Young diagram and a positive integer~$t$. We show that every $t$-Young complex is either contractible or homotopy equivalent to a wedge of spheres. A complete characterization of their vertex-decomposability is provided, and in several cases, we establish explicit formulas for their homotopy types. Interestingly, $t$-Young complexes naturally appear as the Alexander dual complexes of squarefree powers of $t$-path ideals of path graphs, as well as of certain ideals generated by subsets of their minimal generators. As an application, we derive formulas for the projective dimension and Krull dimension of these squarefree powers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13477 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $t$-Young complexes and squarefree powers of $t$-path ideals Navarra, Francesco Qureshi, Ayesha Asloob Veer, Dharm Commutative Algebra Combinatorics 13D02, 05E40, 05E45, 05C70 We introduce a new class of simplicial complexes, called \emph{$t$-Young complexes}, arising from a Young diagram and a positive integer~$t$. We show that every $t$-Young complex is either contractible or homotopy equivalent to a wedge of spheres. A complete characterization of their vertex-decomposability is provided, and in several cases, we establish explicit formulas for their homotopy types. Interestingly, $t$-Young complexes naturally appear as the Alexander dual complexes of squarefree powers of $t$-path ideals of path graphs, as well as of certain ideals generated by subsets of their minimal generators. As an application, we derive formulas for the projective dimension and Krull dimension of these squarefree powers. |
| title | $t$-Young complexes and squarefree powers of $t$-path ideals |
| topic | Commutative Algebra Combinatorics 13D02, 05E40, 05E45, 05C70 |
| url | https://arxiv.org/abs/2511.13477 |