Counting hypermaps by Egorychev's method

Тип публикации: статья из журнала

Год издания: 2016

Идентификатор DOI: 10.1007/s13324-015-0119-z

Ключевые слова: Enumeration, Map, Surface, Orbifold, Rooted hypermap, Unrooted hypermap, Fuchsian group

Аннотация: The aim of this paper is to find explicit formulae for the number of rooted hypermaps with a given number of darts on an orientable surface of genus . Such formulae were obtained earlier for and by Walsh and ArquSs respectively. We first employ the Egorychev's method of counting combinatorial sums to obtain a new version of the ArquSs formula for genus . Then we apply the same approach to get new results for genus . We could do it due to recent results by Giorgetti, Walsh, and Kazarian, Zograf who derived two different, but equivalent, forms of the generating functions for the number of hypermaps of genus two and three.

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Издание

Журнал: ANALYSIS AND MATHEMATICAL PHYSICS

Выпуск журнала: Vol. 6, Is. 3

Номера страниц: 301-314

ISSN журнала: 16642368

Место издания: BASEL

Издатель: SPRINGER BASEL AG

Персоны

Mednykh A. (Siberian Federal University)
Nedela R. (Matej Bel University)

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