Maps in locally orientable surfaces, the double coset algebra, and zonal polynomials

被引:20
作者
Goulden, IP
Jackson, DM
机构
[1] Dept. Combinatorics and Optimization, University of Waterloo, Waterloo, Ont.
来源
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 1996年 / 48卷 / 03期
关键词
D O I
10.4153/CJM-1996-029-x
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页码:569 / 584
页数:16
相关论文
共 19 条
[1]  
[Anonymous], 1983, COMBINATORIAL ENUMER
[2]   ZONAL-POLYNOMIALS AND DOMINO TABLEAUX [J].
BERGERON, N ;
GARSIA, AM .
DISCRETE MATHEMATICS, 1992, 99 (1-3) :3-15
[3]   Connection coefficients, matchings, maps and combinatorial conjectures for Jack symmetric functions [J].
Goulden, IP ;
Jackson, DM .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 348 (03) :873-892
[4]  
GOULDEN IP, 1995, P AM MATH SOC, V123, P995
[5]  
Gross J.L., 1987, Topological Graph Theory
[6]  
Hanlon P J, 1992, Contemp. Math., V138, P151
[7]  
ITZYKSON C, 1990, STAT FIELD THEORY, V2
[8]  
JACK H, 1970, PROC R SOC EDIN A-MA, V69, P1
[9]   A CHARACTER THEORETIC APPROACH TO EMBEDDINGS OF ROOTED MAPS IN AN ORIENTABLE SURFACE OF GIVEN GENUS [J].
JACKSON, DM ;
VISENTIN, TI .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 322 (01) :343-363
[10]   CHARACTER THEORY AND ROOTED MAPS IN AN ORIENTABLE SURFACE OF GIVEN GENUS - FACE-COLORED MAPS [J].
JACKSON, DM ;
VISENTIN, TI .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 322 (01) :365-376