Regular Maps on a Given Surface: A Survey

Širáň‬, Jozef

doi:10.1007/3-540-33700-8_29

Cited by 14 publications

(18 citation statements)

References 29 publications

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“…Foundations of the theory of regular maps have been laid in [4] and [2] and in what follows we just briefly review a few basic facts; for surveys we recommend [7] and [10].…”

Section: Preliminariesmentioning

confidence: 99%

Nonorientable regular maps over linear fractional groups

2012

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It is well known that for any given hyperbolic pair (k, m) there exist infinitely many regular maps of valence k and face length m on an orientable surface, with automorphism group isomorphic to a linear fractional group. A nonorientable analogue of this result was known to be true for all pairs (k, m) as above with at least one even entry. In this paper we establish the existence of such regular maps on nonorientable surfaces for all hyperbolic pairs.

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“…Foundations of the theory of regular maps have been laid in [4] and [2] and in what follows we just briefly review a few basic facts; for surveys we recommend [7] and [10].…”

Section: Preliminariesmentioning

confidence: 99%

Nonorientable regular maps over linear fractional groups

2012

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“…Как известно, это сопоставле-ние определяет взаимно однозначное соответствие между классами изоморфно-сти максимально симметричных ориентированных седловых атомов и классами эквивалентности копредставлений конечных групп с двумя образующими, где вторая образующая имеет порядок 2 (см. на эту тему [6], [2], [3] и [8]). …”

Section: рисunclassified

“…Этот же факт следует и из неравенства Гурвица на порядок группы симметрий правильных карт рода g (см. [8]). Теорема 1.16.…”

Section: рис 10unclassified

“…Вершина 2 не может являться соседней для вершин 4,5,7,8,11,12, следовательно, вершина 2 соединена ребрами с вершинами 1, 3, 6, 9, 10. Используя инвариантность графа смежности относительно симметрии a, мы однозначно восстанавливаем граф смежности.…”

Section: рис 11unclassified

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Максимально Симметричные Клеточные Разбиения Поверхностей И Их Накрытия

Кудрявцева¹,

Kudryavtseva²,

Nikonov³

et al. 2008

Матем. сб.

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“…This leads to the notion of regular maps. Regular maps have also been studied for many years (see for example [8]). …”

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confidence: 99%

Regular Maps of High Density

Eggermont

Hendriks²

2017

Discrete Comput Geom

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A regular map is a surface together with an embedded graph, having properties similar to those of the surface and graph of a platonic solid. We analyze regular maps with reflection symmetry and a simple graph with ratio between vertex-degree and number of vertices strictly exceeding 1 2 . We conclude that all regular maps of this type belong to a family of maps naturally defined on the Fermat curves x n +y n +z n = 0, excepting the one corresponding to the tetrahedron.

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Regular Maps on a Given Surface: A Survey

Cited by 14 publications

References 29 publications

Nonorientable regular maps over linear fractional groups

Nonorientable regular maps over linear fractional groups

Максимально Симметричные Клеточные Разбиения Поверхностей И Их Накрытия

Regular Maps of High Density

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