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Chiral maps of given hyperbolic type
Author(s) -
Conder Marston D. E.,
Hucíková Veronika,
Nedela Roman,
Širáň Jozef
Publication year - 2016
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdv086
Subject(s) - mathematics , type (biology) , base (topology) , permutation (music) , abelian group , combinatorics , simple (philosophy) , graph , pure mathematics , discrete mathematics , mathematical analysis , ecology , philosophy , physics , epistemology , acoustics , biology
We prove the existence of infinitely many orientably‐regular but chiral maps of every given hyperbolic type { m , k } , by constructing base examples from suitable permutation representations of the ordinary ( 2 , k , m ) triangle group, and then taking abelian p ‐covers. The base examples also help to prove that for every pair ( k , m ) of integers with 1 / k + 1 / m ⩽ 1 / 2 , there exist infinitely many regular and infinitely many orientably‐regular but chiral maps of type { m , k } , each with the property that both the map and its dual have simple underlying graph.