Constructions of $k$-regular maps using finite local schemes

Jarosław Buczyński; Tadeusz Januszkiewicz; Joachim Jelisiejew; Mateusz Michałek

doi:10.4171/jems/873

Constructions of $k$-regular maps using finite local schemes

Journal of the European Mathematical Society ◽

10.4171/jems/873 ◽

2019 ◽

Vol 21 (6) ◽

pp. 1775-1808 ◽

Cited By ~ 1

Author(s):

Jarosław Buczyński ◽

Tadeusz Januszkiewicz ◽

Joachim Jelisiejew ◽

Mateusz Michałek

Keyword(s):

Regular Maps ◽

Local Schemes

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Enumeration of rooted 4-regular maps without planar loops

Discrete Mathematics ◽

10.1016/j.disc.2021.112442 ◽

2021 ◽

Vol 344 (8) ◽

pp. 112442

Author(s):

Evgeniy Krasko ◽

Alexander Omelchenko

Keyword(s):

Regular Maps

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Enumeration of unsensed r-regular maps on the projective plane and the Klein bottle

Discrete Mathematics ◽

10.1016/j.disc.2021.112528 ◽

2021 ◽

Vol 344 (11) ◽

pp. 112528

Author(s):

Evgeniy Krasko ◽

Alexander Omelchenko

Keyword(s):

Projective Plane ◽

Klein Bottle ◽

Regular Maps

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Groups PSL(3,p) and nonorientable regular maps

Journal of Algebra ◽

10.1016/j.jalgebra.2008.11.037 ◽

2009 ◽

Vol 321 (5) ◽

pp. 1367-1382 ◽

Cited By ~ 5

Author(s):

Shao-Fei Du ◽

Jin Ho Kwak

Keyword(s):

Regular Maps

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Edge Point Linking by Means of Global and Local Schemes

Signal Processing for Image Enhancement and Multimedia Processing ◽

10.1007/978-0-387-72500-0_11 ◽

2008 ◽

pp. 115-125 ◽

Cited By ~ 2

Author(s):

Angel D. Sappa ◽

Boris X. Vintimilla

Keyword(s):

Edge Point ◽

Global And Local ◽

Local Schemes

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Local geometry of regular maps

10.1017/9781316585085.026 ◽

2021 ◽

pp. 335-358

Keyword(s):

Local Geometry ◽

Regular Maps

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Regular Maps

Generators and Relations for Discrete Groups ◽

10.1007/978-3-662-21946-1_8 ◽

1972 ◽

pp. 101-117

Author(s):

H. S. M. Coxeter ◽

W. O. J. Moser

Keyword(s):

Regular Maps

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Regular Maps

Generators and Relations for Discrete Groups ◽

10.1007/978-3-662-21943-0_8 ◽

1980 ◽

pp. 101-117

Author(s):

H. S. M. Coxeter ◽

W. O. J. Moser

Keyword(s):

Regular Maps

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Regular Maps

Generators and Relations for Discrete Groups ◽

10.1007/978-3-662-25739-5_8 ◽

1957 ◽

pp. 100-117

Author(s):

H. S. M. Coxeter ◽

W. O. J. Moser

Keyword(s):

Regular Maps

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Some regular maps and their polyhedral realizations

DIMACS Series in Discrete Mathematics and Theoretical Computer Science - Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift ◽

10.1090/dimacs/004/12 ◽

1991 ◽

pp. 157-174

Author(s):

H. Coxeter ◽

G. Shephard

Keyword(s):

Regular Maps

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On the Average Number of Trees in Certain Maps

Canadian Journal of Mathematics ◽

10.4153/cjm-1966-006-6 ◽

1966 ◽

Vol 18 ◽

pp. 33-41 ◽

Cited By ~ 9

Author(s):

R. C. Mullin

Keyword(s):

Formal Definition ◽

Root Vertex ◽

Isomorphism Classes ◽

Root Edge ◽

Regular Maps ◽

The Face ◽

Definition Of ◽

Root Face

For a formal definition of “map” the reader is referred to (7, §2). The maps in this paper are rooted by specifying an orientation for one of the edges. This also specifies a root vertex, the negative end of the root, and a root face, the face on the left of the root edge. Counting is, as usual, defined on isomorphism classes.Regular maps of even valence have been enumerated in a recent paper by Tutte. In this paper we determine the average number of trees in such maps, and include similar results for regular tri valent maps, that is, maps with three edges incident on every vertex. In the development for the latter, a formula for the number of trivalent maps with 2t vertices is produced.

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