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 - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public

Place

ZOOM

Abstract

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.