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The multivariate arithmetic Tutte polynomial


Authors: Petter Brändén and Luca Moci
Journal: Trans. Amer. Math. Soc. 366 (2014), 5523-5540
MSC (2010): Primary 05C21; Secondary 05B35, 20K99, 52C35, 82B20
DOI: https://doi.org/10.1090/S0002-9947-2014-06092-3
Published electronically: May 21, 2014
MathSciNet review: 3240933
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Abstract: We introduce an arithmetic version of the multivariate Tutte polynomial and a quasi-polynomial that interpolates between the two. A generalized Fortuin-Kasteleyn representation with applications to arithmetic colorings and flows is obtained. We give a new and more general proof of the positivity of the coefficients of the arithmetic Tutte polynomial and (in the representable case) a geometrical interpretation of them.


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Additional Information

Petter Brändén
Affiliation: Department of Mathematics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
Email: pbranden@kth.se

Luca Moci
Affiliation: Institut de Mathématiques de Jussieu, Université de Paris 7, Bâtiment Sophie Germain, Case 7012, 75205 Paris Cedex 13, France
Email: lucamoci@hotmail.com

DOI: https://doi.org/10.1090/S0002-9947-2014-06092-3
Keywords: Tutte polynomial, multivariate Tutte polynomial, Potts model, toric arrangement, chromatic polynomial, matroid, arithmetic matroid, abelian group, quasi-polynomial
Received by editor(s): October 29, 2012
Received by editor(s) in revised form: January 16, 2013
Published electronically: May 21, 2014
Additional Notes: The first author was a Royal Swedish Academy of Sciences Research Fellow supported by a grant from the Knut and Alice Wallenberg Foundation and was partially supported by the Göran Gustafsson Foundation.
The second author was a Marie Curie Fellow of Istituto Nazionale di Alta Matematica and was partially supported by PRIN 2009 “Spazi di moduli e teoria di Lie”
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.