Powers of generalized binomial edge ideals of path graphs

2023/10/31 by Yi-Huang Shen, Shen, Yi-Huang, Guangjun Zhu +1
Computer Science · Mathematics · #13F20 #13P10 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 13C15 #Secondary 05E40

paper · pdf · doi:10.48550/arxiv.2310.20235

openalex publication_date 2023/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study the powers of the generalized binomial edge ideal J_Km,Pn of a path graph P_n. We explicitly compute their regularities and determine the limit of their depths. We also show that these ordinary powers coincide with their symbolic powers. Additionally, we study the Rees algebra and the special fiber ring of J_Km,Pn via Sagbi basis theory. In particular, we obtain exact formulas for the regularity of these blowup algebras.

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