Chiral hypermaps with few hyperfaces

Rok, strany: 2003, 107 - 128

A hypermap $H$ is a cellular embedding of a $3$@-valent graph into a closed surface cells of which are $3$@-colored (adjacent cells have different colours). The vertices of $H$ are called flags of $H$ and let us denote by $F$ the set of flags. An automorphism of the underlying graph which extends to a colour preserving self-homeomorphism of the surface is called an automorphism of the hypermap. If the surface is orientable, the automorphisms of $H$ split into two classes, orientation preserving and orientation reversing automorphisms. The size of the subgroup of orientation preserving automorphisms is bounded by $|F|/2$ and if the equality is reached, we say that the hypermap is orientably regular. An automorphism of $H$ reversing the global orientation of the surface is called mirror symmetry. Orien tably regular hypermap admitting no mirror symmetries is called chiral. Hence chiral hypermaps have maximum number of orientation preserving symmetries but they are not ``mirror symmetric''. The aim of presented paper is to classify chiral hypermaps with at most four hyperfaces. As these have metacycle oriented monodromy groups, we start first with a construction of an infinite family of chiral hypermaps from metacycle groups.

ISO 690:

D'azevedo, A., Nedela, R. 2003. Chiral hypermaps with few hyperfaces. In Mathematica Slovaca, vol. 53, no.2, pp. 107-128. 0139-9918.

APA:

D'azevedo, A., Nedela, R. (2003). Chiral hypermaps with few hyperfaces. Mathematica Slovaca, 53(2), 107-128. 0139-9918.