Acta Mathematica Vietnamica

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The v-Number of Binomial Edge Ideals

Siddhi Balu Ambhore , Kamalesh Saha , $icon-email$ Indranath Sengupta

Abstract

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 -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 $\emptyset$ . 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.

Acta Mathematica Vietnamica

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The v-Number of Binomial Edge Ideals

Abstract