2023/04/13 by Siddhi Balu Ambhore, Ambhore, Siddhi Balu, Kamalesh Saha +3 · 3 citations
Computer Science · Mathematics · #05C25 #05E40 #13F20 #13F65 #Coding theory and cryptography #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2304.06416
openalex publication_date 2023/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The invariant v-number was introduced very recently in the study of Reed-Muller-type codes. Jaramillo and Villarreal (J Combin. Theory Ser. A 177:105310, 2021) initiated the study of the v-number of edge ideals. Inspired by their work, we take the initiation to study the v-number of binomial edge ideals in this paper. We discuss some properties and bounds of the v-number of binomial edge ideals. We explicitly find the v-number of binomial edge ideals locally at the associated prime corresponding to the cutset ∅. We show that the v-number of Knutson binomial edge ideals is less than or equal to the v-number of their initial ideals. Also, we classify all binomial edge ideals whose v-number is 1. Moreover, we try to relate the v-number with the Castelnuvo-Mumford regularity of binomial edge ideals and give a conjecture in this direction.