Partial-dual Euler-genus distributions for bouquets with small Euler genus

Yan Yang ; Xiaoya Zha

Ars Mathematica Contemporanea, Tome 22 (2022) no. 3, article no. 09, 13 p.

Résumé

For an arbitrary ribbon graph G, the partial-dual Euler-genus polynomial of G is a generating function that enumerates partial duals of G by Euler genus. When G is an orientable ribbon graph, the partial-dual orientable genus polynomial of G is a generating function that enumerates partial duals of G by orientable genus. Gross, Mansour, and Tucker inaugurated these partial-dual Euler-genus and orientable genus distribution problems in 2020. A bouquet is a one-vertex ribbon graph. Given a ribbon graph G, its partial-dual Euler-genus polynomial is the same as that of some bouquet; this motivates our focus on bouquets. We obtain the partial-dual Euler-genus polynomials for all the bouquets with Euler genus at most two.

Détail

DOI : 10.26493/1855-3974.2603.376

Keywords: Ribbon graph, partial dual, Euler-genus polynomial, orientable genus polynomial