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Taylor Ball, Eduardo Camps, Henry Chimal-Dzul, Delio Jaramillo-Velez, Hiram L´ opez, Nathan Nichols, Matthew Perkins, Ivan Soprunov, German Vera-Mart ´ ınez, Gwyn Whieldon, Coding theory package for Macaulay2 , J · 2021

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math.AC 1

years

2025 1

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CONDITIONAL 1

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Comparing the $\mathrm{v}$-number and $h$-polynomials of edge ideals

math.AC · 2025-07-08 · conditional · novelty 7.0

For edge ideals of connected graphs, the v-number can be arbitrarily larger or smaller than the degree of the h-polynomial, their sum is at most the number of vertices, and equality holds exactly for disjoint unions of star graphs.

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  • Comparing the $\mathrm{v}$-number and $h$-polynomials of edge ideals math.AC · 2025-07-08 · conditional · none · ref 2

    For edge ideals of connected graphs, the v-number can be arbitrarily larger or smaller than the degree of the h-polynomial, their sum is at most the number of vertices, and equality holds exactly for disjoint unions of star graphs.