Rationality in map and hypermap enumeration by genus

P. Zograf, M. Kazarian

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Generating functions for a fixed genus map and hypermap enumeration become rational after a simple explicit change of variables. Their numerators are polynomials with integral coefficients that obey a differential recursion, and the denominators are products of powers of explicit linear functions.

Original languageEnglish
Pages (from-to)439-445
Number of pages7
JournalSt. Petersburg Mathematical Journal
Issue number3
Publication statusPublished - 2018
Externally publishedYes


  • Enumeration of hypermaps (Grothendieck's "dessins d'enfants")
  • Enumeration of maps (ribbon graphs)


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