Maps in Locally Orientable Surfaces, the Double Coset Algebra, and Zonal Polynomials
- 1 June 1996
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 48 (3) , 569-584
- https://doi.org/10.4153/cjm-1996-029-x
Abstract
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.Keywords
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