Fatemeh Mohammadi ; Farbod Shokrieh
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Divisors on graphs, Connected flags, and Syzygies
dmtcs:2351 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2013,
DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
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https://doi.org/10.46298/dmtcs.2351
Divisors on graphs, Connected flags, and SyzygiesArticle
Authors: Fatemeh Mohammadi 1; Farbod Shokrieh 2
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Fatemeh Mohammadi;Farbod Shokrieh
1 Fachbereich Mathematik und Informatik [Marburg] [Dept. of Math and Computer Science]
We study the binomial and monomial ideals arising from linear equivalence of divisors on graphs from the point of view of Gröbner theory. We give an explicit description of a minimal Gröbner basis for each higher syzygy module. In each case the given minimal Gröbner basis is also a minimal generating set. The Betti numbers of $I_G$ and its initial ideal (with respect to a natural term order) coincide and they correspond to the number of ``connected flags'' in $G$. Moreover, the Betti numbers are independent of the characteristic of the base field.