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. The multivariate ari ...
Conference paper

The multivariate arithmetic Tutte polynomial

Petter Brändèn (1), Luca Moci ORCID (2)
(1) Department of Mathematics [Stockholm
(2) Department of Mathematics [Roma]
Download article
Open on HAL
Imported on
January 31, 2017
Published on
December 31, 2011
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Proceedings
DOI
10.46298/dmtcs.3072
License
https://about.hal.science/hal-authorisation-v1
Indicators
607
Views
906
Downloads

The multivariate arithmetic Tutte polynomial

Petter Brändèn (1), Luca Moci ORCID (2)
(1) Department of Mathematics [Stockholm
(2) Department of Mathematics [Roma]
Abstract
English
We introduce an arithmetic version of the multivariate Tutte polynomial recently studied by Sokal, and a quasi-polynomial that interpolates between the two. We provide a generalized Fortuin-Kasteleyn representation for representable arithmetic matroids, with applications to arithmetic colorings and flows. We give a new proof of the positivity of the coefficients of the arithmetic Tutte polynomial in the more general framework of pseudo-arithmetic matroids. In the case of a representable arithmetic matroid, we provide a geometric interpretation of the coefficients of the arithmetic Tutte polynomial.
French
Nous introduisons une version arithmétique du polynôme de Tutte multivariée récemment étudié par Sokal, et un quasi-polynôme qui interpole entre les deux. Nous proposons une représentation de Fortuin-Kasteleyn neutralise pour les matroïdes arithmétiques représentables, avec des applications aux colorations et flux arithmétiques. Nous donnons une nouvelle preuve de la positivité des coefficients du polynôme de Tutte arithmétique dans le cadre plus général des matroïdes pseudo-arithmétiques. Dans le cas d'un matroïde arithmétique représentable, nous proposons une interprétation géométrique des coefficients du polynôme de Tutte arithmétique.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • Potts model
  • Tutte polynomial
  • chromatic polynomial
  • matroids
  • arithmetic matroids
  • abelian groups.
Cited by

Source: OpenCitations

  • On powers of Plücker coordinates and representability of arithmetic matroids

    Advances in Applied Mathematics

    Authors : Matthias Lenz

    Journal reference : Volume 112, 2019, pp. 101911

    DOI : 10.1016/j.aam.2019.04.008
  • Splines, lattice points, and arithmetic matroids

    arXiv (Cornell University)

    Authors : Matthias Lenz

    Journal reference : Volume 43, 2015, pp. 277-324

    DOI : 10.1007/s10801-015-0621-2
  • Cohomology of complements of toric arrangements associated with root systems

    Research in the Mathematical Sciences

    Authors : Olof Bergvall ORCID

    Journal reference : Volume 9, 2022, pp.

    DOI : 10.1007/s40687-021-00305-z
  • Eulerian polynomials for subarrangements of Weyl arrangements

    arXiv (Cornell University)

    Authors : Ahmed Umer Ashraf, Tan Nhat Tran ORCID, Masahiko Yoshinaga

    Journal reference : Volume 120, 2020, pp. 102064

    DOI : 10.1016/j.aam.2020.102064
  • On the cohomology of arrangements of subtori

    Journal of the London Mathematical Society

    Authors : Luca Moci ORCID, Roberto Pagaria ORCID

    Journal reference : Volume 106, 2022, pp. 1999-2029

    DOI : 10.1112/jlms.12616
  • Products of arithmetic matroids and quasipolynomial invariants of CW-complexes

    Archivio istituzionale della ricerca (Alma Mater Studiorum Università di Bologna)

    Authors : Emanuele Delucchi ORCID, Luca Moci ORCID

    Journal reference : Volume 157, 2018, pp. 28-40

    DOI : 10.1016/j.jcta.2018.01.005
  • An equivalent formulation of chromatic quasi-polynomials

    arXiv (Cornell University)

    Authors : Tan Nhat Tran ORCID

    Journal reference : Volume 343, 2020, pp. 112012

    DOI : 10.1016/j.disc.2020.112012
  • Period Collapse in Characteristic Quasi-Polynomials of Hyperplane Arrangements

    International Mathematics Research Notices

    Authors : Akihiro Higashitani ORCID, Tan Nhat Tran ORCID, Masahiko Yoshinaga ORCID

    Journal reference : Volume 2023, 2022, pp. 8934-8963

    DOI : 10.1093/imrn/rnac104
  • Cohomology ring of non‐compact abelian arrangements

    Archivio istituzionale della ricerca (Alma Mater Studiorum Università di Bologna)

    Authors : E. Bazzocchi, R. Pagaria ORCID, M. Pismataro

    Journal reference : Volume 131, 2025, pp.

    DOI : 10.1112/plms.70113
  • The integer cohomology algebra of toric arrangements

    arXiv (Cornell University)

    Authors : Filippo Callegaro ORCID, Emanuele Delucchi ORCID

    Journal reference : Volume 313, 2017, pp. 746-802

    DOI : 10.1016/j.aim.2017.04.017
  • Polyhedra and parameter spaces for matroids over valuation rings

    Advances in Mathematics

    Authors : Alex Fink ORCID, Luca Moci ORCID

    Journal reference : Volume 343, 2018, pp. 448-494

    DOI : 10.1016/j.aim.2018.11.009
  • Convolution formulas for multivariate arithmetic Tutte polynomials

    Advances in Applied Mathematics

    Authors : Tianlong Ma, Xian'an Jin, Weiling Yang

    Journal reference : Volume 157, 2024, pp. 102692

    DOI : 10.1016/j.aam.2024.102692
  • G-Tutte Polynomials and Abelian Lie Group Arrangements

    arXiv (Cornell University)

    Authors : Ye Liu, Tan Nhat Tran, Masahiko Yoshinaga

    Journal reference : Volume 2021, 2019, pp. 150-188

    DOI : 10.1093/imrn/rnz092
  • Representations of torsion-free arithmetic matroids

    arXiv (Cornell University)

    Authors : Roberto Pagaria ORCID, Giovanni Paolini ORCID

    Journal reference : Volume 93, 2020, pp. 103272

    DOI : 10.1016/j.ejc.2020.103272
  • Orientable arithmetic matroids

    arXiv (Cornell University)

    Authors : Roberto Pagaria ORCID

    Journal reference : Volume 343, 2020, pp. 111872

    DOI : 10.1016/j.disc.2020.111872
  • Combinatorics of certain abelian Lie group arrangements and chromatic quasi-polynomials

    Journal of Combinatorial Theory Series A

    Authors : Tan Nhat Tran ORCID, Masahiko Yoshinaga ORCID

    Journal reference : Volume 165, 2019, pp. 258-272

    DOI : 10.1016/j.jcta.2019.02.003
  • Matroids Over a Ring

    Springer INdAM series

    Authors : Alex Fink ORCID, Luca Moci ORCID

    Journal reference : Volume , 2015, pp. 41-47

    DOI : 10.1007/978-3-319-20155-9_9
  • The Arithmetic Tutte polynomial of two matrices associated to Trees

    Special Matrices

    Authors : R. B. Bapat ORCID, Sivaramakrishnan Sivasubramanian ORCID

    Journal reference : Volume 6, 2018, pp. 310-322

    DOI : 10.1515/spma-2018-0026
  • Universal Tutte characters via combinatorial coalgebras

    Algebraic Combinatorics

    Authors : Clément Dupont ORCID, Alex Fink ORCID, Luca Moci ORCID

    Journal reference : Volume 1, 2018, pp. 603-651

    DOI : 10.5802/alco.35
  • Representations of Weakly Multiplicative Arithmetic Matroids are Unique

    arXiv (Cornell University)

    Authors : Matthias Lenz

    Journal reference : Volume 23, 2019, pp. 335-346

    DOI : 10.1007/s00026-019-00424-z
  • The monoid of monotone functions on a poset and quasi-arithmetic multiplicities for uniform matroids

    arXiv (Cornell University)

    Authors : Winfried Bruns ORCID, Pedro A. García-Sánchez ORCID, Luca Moci ORCID

    Journal reference : Volume 569, 2020, pp. 377-400

    DOI : 10.1016/j.jalgebra.2020.10.026
  • Geometric Realizations and Duality for Dahmen–Micchelli Modules and De Concini–Procesi–Vergne Modules

    Discrete & Computational Geometry

    Authors : Francesco Cavazzani, Luca Moci ORCID

    Journal reference : Volume 55, 2015, pp. 74-99

    DOI : 10.1007/s00454-015-9745-3
  • The homotopy type of elliptic arrangements

    arXiv (Cornell University)

    Authors : Emanuele Delucchi, Roberto Pagaria

    Journal reference : Volume 21, 2021, pp. 2037-2063

    DOI : 10.2140/agt.2021.21.2037
  • Poincaré polynomial of elliptic arrangements is not determined by the Tutte polynomial

    Discrete Mathematics

    Authors : Roberto Pagaria ORCID

    Journal reference : Volume 343, 2019, pp. 111710

    DOI : 10.1016/j.disc.2019.111710
  • Group actions on semimatroids

    arXiv (Cornell University)

    Authors : Emanuele Delucchi ORCID, Sonja Riedel

    Journal reference : Volume 95, 2017, pp. 199-270

    DOI : 10.1016/j.aam.2017.11.001
  • Two examples of toric arrangements

    Journal of Combinatorial Theory Series A

    Authors : Roberto Pagaria ORCID

    Journal reference : Volume 167, 2019, pp. 389-402

    DOI : 10.1016/j.jcta.2019.05.006
  • Centering toric arrangements of maximal rank

    Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica

    Authors : Elia Saini

    Journal reference : Volume 23, 2024, pp. 39-46

    DOI : 10.2478/aupcsm-2024-0005
Preview
Loading PDF preview...