2013/01/31 by Isabel Hubard, Hubard, Isabel, Alen Orbanić +5 · 2 citations
Mathematics · #05B45 #05C25 #05C30 #52B15 #57M05 #68E10 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1301.7637
openalex publication_date 2013/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A k-orbit map is a map with its automorphism group partitioning the set of flags into k orbits. Recently k-orbit maps were studied by Orbani' c, Pellicer and Weiss, for k ≤ 4. In this paper we use symmetry type graphs to extend such study and classify all the types of 5-orbit maps, as well as all self-dual, properly and improperly, symmetry type of k-orbit maps with k≤ 7. Moreover, we determine, for small values of k, all types of k-orbits maps that are medial maps. Self-dualities constitute an important tool in this quest.