Fatemeh Mohammadi ; Farbod Shokrieh - 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) - https://doi.org/10.46298/dmtcs.2351
Divisors on graphs, Connected flags, and Syzygies

Authors: Fatemeh Mohammadi ORCID-iD1; Farbod Shokrieh 2

  • 1 Fachbereich Mathematik und Informatik [Marburg] [Dept. of Math and Computer Science]
  • 2 Georgia Institute of Technology [Atlanta]

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.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: Graph,divisors,chip-firing,Gröbner bases,Betti numbers,connected flags.,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Connections Between Number Theory, Algebraic Geometry, and Combinatorics; Funder: National Science Foundation; Code: 0901487

Linked publications - datasets - softwares

Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.aim.2007.04.012
  • 10.1016/j.aim.2007.04.012
Riemann–Roch and Abel–Jacobi theory on a finite graph

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