English

Medial symmetry type graphs

Combinatorics 2013-02-01 v1

Abstract

A kk-orbit map is a map with its automorphism group partitioning the set of flags into kk orbits. Recently kk-orbit maps were studied by Orbani\' c, Pellicer and Weiss, for k4k \leq 4. In this paper we use symmetry type graphs to extend such study and classify all the types of 55-orbit maps, as well as all self-dual, properly and improperly, symmetry type of kk-orbit maps with k7k\leq 7. Moreover, we determine, for small values of kk, all types of kk-orbits maps that are medial maps. Self-dualities constitute an important tool in this quest.

Keywords

Cite

@article{arxiv.1301.7637,
  title  = {Medial symmetry type graphs},
  author = {Isabel Hubard and Alen Orbanić and Tomaž Pisanski and María del Río Francos},
  journal= {arXiv preprint arXiv:1301.7637},
  year   = {2013}
}
R2 v1 2026-06-21T23:18:37.625Z