Divisors on graphs, Connected flags, and Syzygies

Fatemeh Mohammadi 1 Farbod Shokrieh 2
1 Fachbereich Mathematik und Informatik [Marburg] [Dept. of Math and Computer Science]
2 Georgia Institute of Technology [Atlanta]
Abstract : 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.
Keywords : Graph divisors chip-firing Gröbner bases Betti numbers connected flags.
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Communication dans un congrès
Alain Goupil and Gilles Schaeffer. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), pp.885-896, 2013, DMTCS Proceedings
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Fatemeh Mohammadi, Farbod Shokrieh. Divisors on graphs, Connected flags, and Syzygies. Alain Goupil and Gilles Schaeffer. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), pp.885-896, 2013, DMTCS Proceedings. 〈hal-01229678〉

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