Maps in Locally Orientable Surfaces, the Double Coset Algebra, and Zonal Polynomials

Goulden, I. P. ; Jackson, D. M.

Canadian journal of mathematics, Tome 48 (1996) no. 3, pp. 569-584

Résumé

The genus series is the generating series for the number of maps (inequivalent two-cell embeddings of graphs), in locally orientable surfaces, closed and without boundary, with respect to vertex- and face-degrees, number of edges and genus. A hypermap is a face two-colourable map. An expression for the genus series for (rooted) hypermaps is derived in terms of zonal polynomials by using a double coset algebra in conjunction with an encoding of a map as a triple of matchings. The expression is analogous to the one obtained for orientable surfaces in terms of Schur functions.

Détail

DOI : 10.4153/CJM-1996-029-x

Mots-clés : 05E05, 05A15, 57M15

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