Skip to main contentSkip to search
Episciences
Open Access Journals
Sign in(new window)
Discrete Mathematics & Theoretical Computer Science logo
Discrete Mathematics & Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science logo
Discrete Mathematics & Theoretical Computer Science
Sign in(new window)
Articles & Issues
All articlesAll accepted articlesAll volumesLast volumeSectionsSpecial issuesAuthors
About
The journalIndexing
Boards
Publish
For authorsEthical charter
Submit
Discrete Mathematics & Theoretical Computer Science logo
Contact
|
Credits
eISSN 1365-8050
|
RSS
|
Atom
Episciences
Documentation
|
Acknowledgements
|
Publishing policy
Accessibility: non-compliant
|
Legal mentions
|
Privacy statement
|
Terms of use
  1. Home > Articles & Issues >
  2. Articles >
  3. Divisors on graphs, ...
Conference paper

Divisors on graphs, Connected flags, and Syzygies

Fatemeh Mohammadi ORCID (1), Farbod Shokrieh (2)
(1) Fachbereich Mathematik und Informatik [Marburg] [Dept. of Math and Computer Science]
(2) Georgia Institute of Technology [Atlanta]
Download article
Open on HAL
Imported on
November 21, 2016
Published on
December 31, 2012
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Proceedings
DOI
10.46298/dmtcs.2351
License
https://about.hal.science/hal-authorisation-v1
National Science Foundation
0901487
Connections Between Number Theory, Algebraic Geometry, and Combinatorics
Indicators
787
Views
936
Downloads

Divisors on graphs, Connected flags, and Syzygies

Fatemeh Mohammadi ORCID (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
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • Graph
  • divisors
  • chip-firing
  • Gröbner bases
  • Betti numbers
  • connected flags.
Cited by

Source: OpenCitations

  • Fourientations and the Tutte polynomial

    Research in the Mathematical Sciences

    Authors : Spencer Backman, Sam Hopkins

    Journal reference : Volume 4, 2017, pp.

    DOI : 10.1186/s40687-017-0107-z

  • Types of signature analysis in reliability based on Hilbert series

    Journal of Symbolic Computation

    Authors : Fatemeh Mohammadi ORCID, Eduardo Sáenz-de-Cabezón ORCID, Henry P. Wynn ORCID

    Journal reference : Volume 79, 2016, pp. 140-155

    DOI : 10.1016/j.jsc.2016.08.010

  • The Algebraic Method in Tree Percolation

    arXiv (Cornell University)

    Authors : Fatemeh Mohammadi ORCID, Eduardo Sáenz-de-Cabezón ORCID, Henry P. Wynn ORCID

    Journal reference : Volume 30, 2016, pp. 1193-1212

    DOI : 10.1137/151003647

  • Redundancy analysis using lcm-filtrations: networks, system signature and sensitivity evaluation

    London School of Economics and Political Science Theses Online (London School of Economics and Political Science)

    Authors : Fatemeh Mohammadi ORCID, Eduardo Sáenz-de-Cabezón ORCID, Henry Wynn ORCID

    Journal reference : Volume , 2025, pp. 293-301

    DOI : 10.1145/3747199.3747573

  • Minimal resolutions of lattice ideals

    Journal of Pure and Applied Algebra

    Authors : Yupeng Li ORCID, Ezra Miller ORCID, Erika Ordog

    Journal reference : Volume 229, 2025, pp. 107901

    DOI : 10.1016/j.jpaa.2025.107901

  • Prime splittings of determinantal ideals

    arXiv (Cornell University)

    Authors : Fatemeh Mohammadi, Johannes Rauh

    Journal reference : Volume 46, 2018, pp. 2278-2296

    DOI : 10.1080/00927872.2018.1427241

  • Minimal cellular resolutions of powers of matching field ideals

    Journal of Pure and Applied Algebra

    Authors : Oliver Clarke ORCID, Fatemeh Mohammadi ORCID

    Journal reference : Volume 229, 2025, pp. 107893

    DOI : 10.1016/j.jpaa.2025.107893

  • An integer sequence and standard monomials

    Journal of Algebra and Its Applications

    Authors : Ajay Kumar ORCID, Chanchal Kumar

    Journal reference : Volume 17, 2017, pp. 1850037

    DOI : 10.1142/s0219498818500378

  • Minimal free resolutions of lattice ideals of digraphs

    Algebraic Combinatorics

    Authors : Liam O’Carroll, Francesc Planas-Vilanova ORCID

    Journal reference : Volume 1, 2018, pp. 283-326

    DOI : 10.5802/alco.15

  • Divisors on graphs, binomial and monomial ideals, and cellular resolutions

    arXiv (Cornell University)

    Authors : Fatemeh Mohammadi, Farbod Shokrieh

    Journal reference : Volume 283, 2015, pp. 59-102

    DOI : 10.1007/s00209-015-1589-2
Preview
Loading PDF preview...