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- Title
Orientably Regular Maps of Given Hyperbolic Type with No Non-trivial Exponents.
- Authors
Bachratá, Veronika; Bachratý, Martin
- Abstract
Given an orientable map M , and an integer e relatively prime to the valency of M , the eth rotational power M e of M is the map formed by replacing the cyclic rotation of edges around each vertex with its eth power. If M and M e are isomorphic, and the corresponding isomorphism preserves the orientation of the carrier surface, then we say that e is an exponent of M .In this paper, we use canonical regular covers of maps to prove that for every given hyperbolic pair (k, m) there exists an orientably regular map of type { m , k } with no non-trivial exponents. As an application we show that for every given hyperbolic pair (k, m) there exist infinitely many orientably regular maps of type { m , k } with no non-trivial exponents, each with the property that the map and its dual have simple underlying graph.
- Subjects
EXPONENTS; MAPS; VALENCE (Chemistry); REGULAR graphs; INTEGERS; ROTATIONAL motion; HYPERBOLIC groups
- Publication
Annals of Combinatorics, 2023, Vol 27, Issue 2, p353
- ISSN
0218-0006
- Publication type
Article
- DOI
10.1007/s00026-022-00603-5