A rooted map invariant, non-orientability and Jack symmetric functions

DOI10.1016/j.jctb.2006.07.007zbMath1119.05027OpenAlexW2063442271MaRDI QIDQ875947

Daniel R. L. Brown, David M. Jackson

Publication date: 16 April 2007

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jctb.2006.07.007

zbMATH Keywords

Jack symmetric functionsEuler characteristicLaplace-Beltrami operatororientabilityrooted mapsmap enumerationdepth first search

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Enumeration in graph theory (05C30) Planar graphs; geometric and topological aspects of graph theory (05C10)

Related Items (8)

On the matchings-Jack conjecture for Jack connection coefficients indexed by two single part partitions ⋮ Macdonald cumulants, \(G\)-inversion polynomials and \(G\)-parking functions ⋮ A labelled variant of the matchings-Jack and hypermap-Jack conjectures ⋮ Top degree part in \(b\)-conjecture for unicellular bipartite maps ⋮ Cumulants of Jack symmetric functions and the $b$-conjecture ⋮ Unnamed Item ⋮ Non-orientable branched coverings, \(b\)-Hurwitz numbers, and positivity for multiparametric Jack expansions ⋮ Combinatorial and algebraic enumeration: a survey of the work of Ian P. Goulden and David M. Jackson

Uses Software

• SF

Cites Work

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• A recursion and a combinatorial formula for Jack polynomials
• A Maple package for symmetric functions
• Counting rooted maps by genus. I
• A geometric parametrization for the virtual Euler characteristics of the moduli spaces of real and complex algebraic curves
• Determinants of Random Matrices and Jack Polynomials of Rectangular Shape
• A Census of Slicings
• Connection coefficients, matchings, maps and combinatorial conjectures for Jack symmetric functions

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