Geodesic
A lattice point counting generalisation of the Tutte polynomial
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020).

Voir la notice de l'article provenant de la source Episciences

The Tutte polynomial for matroids is not directly applicable to polymatroids. For instance, deletion- contraction properties do not hold. We construct a polynomial for polymatroids which behaves similarly to the Tutte polynomial of a matroid, and in fact contains the same information as the Tutte polynomial when we restrict to matroids. This polynomial is constructed using lattice point counts in the Minkowski sum of the base polytope of a polymatroid and scaled copies of the standard simplex. We also show that, in the matroid case, our polynomial has coefficients of alternating sign, with a combinatorial interpretation closely tied to the Dawson partition. 
@article{DMTCS_2020_special_379_a13,
     author = {Cameron, Amanda and Fink, Alex},
     title = {A lattice point counting generalisation of the {Tutte} polynomial},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     year = {2020},
     doi = {10.46298/dmtcs.6331},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6331/}
}
TY  - JOUR
AU  - Cameron, Amanda
AU  - Fink, Alex
TI  - A lattice point counting generalisation of the Tutte polynomial
JO  - Discrete mathematics & theoretical computer science
PY  - 2020
VL  - DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6331/
DO  - 10.46298/dmtcs.6331
LA  - en
ID  - DMTCS_2020_special_379_a13
ER  - 
%0 Journal Article
%A Cameron, Amanda
%A Fink, Alex
%T A lattice point counting generalisation of the Tutte polynomial
%J Discrete mathematics & theoretical computer science
%D 2020
%V DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6331/
%R 10.46298/dmtcs.6331
%G en
%F DMTCS_2020_special_379_a13
Cameron, Amanda; Fink, Alex. A lattice point counting generalisation of the Tutte polynomial. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi : 10.46298/dmtcs.6331. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6331/

Cité par Sources :