2023/04/23 by Bijender, Kumar, Ajay, Kumar, Rajiv
#05E40 #13C14 #13D02 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2304.11630
In 2011, Herzog, Hibi, and Ohsugi conjectured that if J is the cover ideal of a chordal graph, then Js is componentwise linear for all s ≥ 1. In 2022, Hà and Tuyl considered objects more general than chordal graphs and posed the following problem: Let J(Δ) be the cover ideal of a simplicial tree Δ. Is it true that J(Δ)s is componentwise linear for all s ≥ 1? In this article, we give an affirmative answer to this problem.