2023/06/03 by Ajay Kumar, Arvind Kumar, Kumar, Ajay +1
Mathematics · Medicine · #Commutative Algebra and Its Applications #Graph theory and applications #Cholinesterase and Neurodegenerative Diseases
paper · pdf · doi:10.48550/arxiv.2306.01994
In this article, we study the linearity of the minimal free resolution of powers of facets ideals of simplicial trees. We give a complete characterization of simplicial trees for which (some) power of its facet ideal has a linear resolution. We calculate the regularity of the t-path ideal of a perfect rooted tree. We also obtain an upper bound for the regularity of the t-path ideal of a rooted tree. We give a procedure to calculate the regularity of powers of facet ideals of simplicial trees. As a consequence of this result, we study the regularity of powers of t-path ideals of rooted trees. We pose a regularity upper bound conjecture for facet ideals of simplicial trees, which is as follows: if Δ is a d-dimensional simplicial tree, then \reg(I(Δ)s) ≤ (d+1)(s-1)+\reg(I(Δ)) for all s ≥ 1. We prove this conjecture for some special classes of simplicial trees.