Geodesic
The Hopf monoid of hypergraphs and its sub-monoids: basic invariant and reciprocity theorem
Jean-Christophe Aval ; Théo Karaboghossian1 ; Adrian Tanasa2
1Université de Bordeaux
2Université de Bordeaux, Labri; IUF Paris; H. Hulubei Nat. Inst. Phys. Nucl. Engineering Magurele, Romania
The electronic journal of combinatorics, Tome 27 (2020) no. 1
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

In arXiv:1709.07504 Aguiar and Ardila give a Hopf monoid structure on hypergraphs as well as a general construction of polynomial invariants on Hopf monoids. Using these results, we define in this paper a new polynomial invariant on hypergraphs. We give a combinatorial interpretation of this invariant on negative integers which leads to a reciprocity theorem on hypergraphs. Finally, we use this invariant to recover well-known invariants on other combinatorial objects (graphs, simplicial complexes, building sets, etc) as well as the associated reciprocity theorems.
DOI : 10.37236/8740
Classification : 05C65, 05C25, 05C15, 16T05, 05E45
Mots-clés : polynomial invariants on Hopf monoids, reciprocity theorem on hypergraphs

Jean-Christophe Aval    ; Théo Karaboghossian  1   ; Adrian Tanasa  2

1 Université de Bordeaux
2 Université de Bordeaux, Labri; IUF Paris; H. Hulubei Nat. Inst. Phys. Nucl. Engineering Magurele, Romania 
@article{10_37236_8740,
     author = {Jean-Christophe Aval and Th\'eo Karaboghossian and Adrian Tanasa},
     title = {The {Hopf} monoid of hypergraphs and its sub-monoids: basic invariant and reciprocity theorem},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {1},
     doi = {10.37236/8740},
     zbl = {1434.05100},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8740/}
}
TY  - JOUR
AU  - Jean-Christophe Aval
AU  - Théo Karaboghossian
AU  - Adrian Tanasa
TI  - The Hopf monoid of hypergraphs and its sub-monoids: basic invariant and reciprocity theorem
JO  - The electronic journal of combinatorics
PY  - 2020
VL  - 27
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/8740/
DO  - 10.37236/8740
ID  - 10_37236_8740
ER  - 
%0 Journal Article
%A Jean-Christophe Aval
%A Théo Karaboghossian
%A Adrian Tanasa
%T The Hopf monoid of hypergraphs and its sub-monoids: basic invariant and reciprocity theorem
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/8740/
%R 10.37236/8740
%F 10_37236_8740
Jean-Christophe Aval; Théo Karaboghossian; Adrian Tanasa. The Hopf monoid of hypergraphs and its sub-monoids: basic invariant and reciprocity theorem. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8740

Cité par Sources :