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

Autor:	David M. Jackson, Ian P. Goulden
Rok vydání:	1996
Předmět:	Combinatorics Algebra Vertex (graph theory) Double coset General Mathematics 010102 general mathematics 0103 physical sciences Generating series 010307 mathematical physics 0101 mathematics 01 natural sciences Mathematics
Zdroj:	Canadian Journal of Mathematics. 48:569-584
ISSN:	1496-4279 0008-414X
DOI:	10.4153/cjm-1996-029-x
Popis:	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.
Databáze:	OpenAIRE
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