On squarefree powers of simplicial trees

Elshani Kamberi; Francesco Navarra; Ayesha Asloob Qureshi

doi:10.1016/j.jalgebra.2026.01.008

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arXiv · 2406.13670

On squarefree powers of simplicial trees

Elshani Kamberi·Francesco Navarra·Ayesha Asloob Qureshi

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Abstract

In this article, we study the squarefree powers of facet ideals associated with simplicial trees. Specifically, we examine the linearity of their minimal free resolution and their regularity. Additionally, we investigate when the first syzygy module of squarefree powers of a simplicial tree is generated by linear relations. Finally, we provide a combinatorial formula for the regularity of the squarefree powers of $t$-path ideals of path graphs.

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Elshani Kamberi, Francesco Navarra, Ayesha Asloob Qureshi. 2024-06-19. On squarefree powers of simplicial trees. https://doi.org/10.1016/j.jalgebra.2026.01.008

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