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Sibirskii Matematicheskii Zhurnal, 2013, Volume 54, Number 4, Pages 788–806 (Mi smj2458)  
This article is cited in 2 scientific papers (total in 2 papers)

On the enumeration of circular maps with given number of edges

M. A. Deryaginaa, A. D. Mednykhab

a Novosibirsk State University, Novosibirsk, Russia
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Full-text PDF (583 kB) Citations (2)
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Abstract: A map is a closed Riemann surface $S$ with an embedded graph $G$ such that $S\setminus G$ is homeomorphic to a disjoint union of open disks. Tutte began a systematic study of maps in the 1960s, and contemporary authors are actively developing it. We introduce the concept of circular map and establish its equivalence to the concept of map admitting a coloring of the faces in two colors. The main result is a formula for the number of circular maps with given number of edges.
Keywords: circular map, Riemann surface, branched covering, two-color map.
Received: 17.09.2012
English version:
Siberian Mathematical Journal, 2013, Volume 54, Issue 4, Pages 624–639
DOI: https://doi.org/10.1134/S0037446613040058
Bibliographic databases:
Document Type: Article
UDC: 517.545+519.111
Language: Russian
Citation: M. A. Deryagina, A. D. Mednykh, “On the enumeration of circular maps with given number of edges”, Sibirsk. Mat. Zh., 54:4 (2013), 788–806; Siberian Math. J., 54:4 (2013), 624–639
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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