Eight times four bialgebras of hypergraphs, cointeractions, and chromatic polynomials

Seminar
Speaker
Gunnar Fløystad (U Bergen)
Date
07/07/2024 - 15:30 - 14:05Add to Calendar 2024-07-07 14:05:00 2024-07-07 15:30:00 Eight times four bialgebras of hypergraphs, cointeractions, and chromatic polynomials Link to the recording   The bialgebra of hypergraphs is shown to have a cointeracting bialgebra structure.  We show that the associated polynomial is the hypergraph chromatic polynomial.  Moreover, hypergraphs occur in quartets: there is a dual, a complement, and a dual complement hypergraph.  These correspondences are involutions and give rise to three other double bialgebras, and three more chromatic polynomials.  In all we give eight quartets of bialgebras which includes recent bialgebras introduced by  Aguiar and  Ardila, and by Foissy.   ZOOM אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
ZOOM
Abstract
 
The bialgebra of hypergraphs is shown to have a cointeracting bialgebra structure. 
We show that the associated polynomial is the hypergraph chromatic polynomial. 
Moreover, hypergraphs occur in quartets: there is a dual, a complement, and a dual complement hypergraph. 
These correspondences are involutions and give rise to three other double bialgebras, and three more chromatic polynomials. 
In all we give eight quartets of bialgebras which includes recent bialgebras introduced by  Aguiar and  Ardila, and by Foissy.

 

Last Updated Date : 09/07/2024