Rationality in map and hypermap enumeration by genus

  title={Rationality in map and hypermap enumeration by genus},
  author={M. Kazarian and P. Zograf},
  journal={arXiv: Combinatorics},
  • M. Kazarian, P. Zograf
  • Published 2016
  • Mathematics
  • arXiv: Combinatorics
  • Generating functions for a fixed genus map and hypermap enumeration become rational after a simple explicit change of variables. Their numerators are polynomials with integer coefficients that obey a differential recursion, and denominators are products of powers of explicit linear functions. 
    4 Citations


    Counting rooted maps by genus II
    • 179
    Enumeration of hypermaps of a given genus
    • 4
    • PDF
    Hypermaps versus bipartite maps
    • 180
    Counting cycles in permutations by group characters, with an application to a topological problem
    • 99
    • PDF
    Simple recurrence formulas to count maps on orientable surfaces
    • 22
    • PDF
    Enumeration of unrooted maps of a given genus
    • 60
    • PDF
    Enumeration of unrooted hypermaps of a given genus
    • 25
    • PDF
    Enumeration of Grothendieck's dessins and KP hierarchy
    • 51
    • PDF
    Graphs on Surfaces and Their Applications
    • 613