English

Pattern occurrences in random planar maps

Combinatorics 2019-05-20 v2 Probability

Abstract

We consider planar maps adjusted with a (regular critical) Boltzmann distribution and show that the expected number of pattern occurrences of a given map is asymptotically linear when the number n of edges goes to infinity. The main ingredient for the proof is an extension of a formula by Liskovets (1999).

Keywords

Cite

@article{arxiv.1801.10007,
  title  = {Pattern occurrences in random planar maps},
  author = {Michael Drmota and Benedikt Stufler},
  journal= {arXiv preprint arXiv:1801.10007},
  year   = {2019}
}
R2 v1 2026-06-23T00:03:38.692Z