2023/08/29 by Hà Minh Lam, Lam, Ha Minh, Ngô Viêt Trung +3 · 1 citation
Chemistry · Mathematics · Medicine · #05E40 (Secondary) #13C05 #13C15 (Primary) 05C70 #Cholinesterase and Neurodegenerative Diseases #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Synthesis and pharmacology of benzodiazepine derivatives
paper · pdf · doi:10.48550/arxiv.2308.15021
openalex publication_date 2023/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By a classical result of Brodmann, the function depth R/It is asymptotically a constant, i.e. there is a number s such that depth R/It = depth R/Is for t > s. One calls the smallest number s with this property the index of depth stability of I and denotes it by dstab(I). This invariant remains mysterious til now. The main result of this paper gives an explicit formula for dstab(I) when I is an arbitrary ideal generated by squarefree monomials of degree 2. That is the first general case where one can characterize dstab(I) explicitly. The formula expresses dstab(I) in terms of the associated graph. The proof involves new techniques which relate different topics such as simplicial complexes, systems of linear inequalities, graph parallelizations, and ear decompositions. It provides an effective method for the study of powers of edge ideals.