Geodesic
Highly symmetric maps on surfaces with boundary
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part V, Tome 446 (2016), pp. 100-121
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The regular maps and the arc-transitive maps on surfaces with non-empty boundary are classified. It is shown that it is unrealistic to expect a similar classification of edge-transitive maps on such surfaces. 
@article{ZNSL_2016_446_a5,
     author = {G. A. Jones},
     title = {Highly symmetric maps on surfaces with boundary},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {100--121},
     year = {2016},
     volume = {446},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_446_a5/}
}
TY  - JOUR
AU  - G. A. Jones
TI  - Highly symmetric maps on surfaces with boundary
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2016
SP  - 100
EP  - 121
VL  - 446
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2016_446_a5/
LA  - en
ID  - ZNSL_2016_446_a5
ER  - 
%0 Journal Article
%A G. A. Jones
%T Highly symmetric maps on surfaces with boundary
%J Zapiski Nauchnykh Seminarov POMI
%D 2016
%P 100-121
%V 446
%U http://geodesic.mathdoc.fr/item/ZNSL_2016_446_a5/
%G en
%F ZNSL_2016_446_a5
G. A. Jones. Highly symmetric maps on surfaces with boundary. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part V, Tome 446 (2016), pp. 100-121. http://geodesic.mathdoc.fr/item/ZNSL_2016_446_a5/

[1] R. P. Bryant, D. Singerman, “Foundations of the theory of maps on surfaces with boundary”, Q. J. Math. Oxford, 36:2 (1985), 17–41 | DOI | MR | Zbl

[2] M. D. E. Conder, “Regular maps and hypermaps of Euler characteristic $-1$ to $-200$”, J. Combin. Theory Ser. B, 99 (2009), 455–459 With associated lists of computational data available at http://www.math.auckland.ac.nz/~conder/hypermaps.html | DOI | MR | Zbl

[3] R. Cori, Un code pour les graphes planaires et ses applications, Astérisque, 27, Soc. Math. France, Paris, 1975 | MR

[4] H. S. M. Coxeter, W. O. J. Moser, Generators and Relations for Discrete Groups, Springer, Berlin–Heidelberg–New York, 1980 | MR | Zbl

[5] E. Girondo, G. González–Diez, Introduction to Compact Riemann Surfaces and Dessins d'Enfants, London Math. Soc. Student Texts, 79, Cambridge University Press, Cambridge, 2012 | MR | Zbl

[6] J. E. Graver, M. E. Watkins, Locally finite, planar, edge-transitive graphs, Mem. Amer. Math. Soc., 126, no. 601, 1997 | MR

[7] A. Grothendieck, “Esquisse d'un Programme”, Geometric Galois Actions, v. I, London Math. Soc. Lecture Note Ser., 242, Around Grothendieck's Esquisse d'un Programme, eds. P. Lochak, L. Schneps, Cambridge University Press, Cambridge, 1997, 5–48 | MR | Zbl

[8] P. Hall, “The Eulerian functions of a group”, Q. J. Math., 7 (1936), 134–151 | DOI | Zbl

[9] G. A. Jones, J. S. Thornton, “Operations on maps, and outer automorphisms”, J. Combin. Theory Ser. B, 35 (1983), 93–103 | DOI | MR | Zbl

[10] B. Köck, D. Singerman, “Real Belyi theory”, Q. J. Math., 58 (2007), 463–478 | DOI | MR | Zbl

[11] S. K. Lando, A. K. Zvonkin, Graphs on Surfaces and Their Applications, Springer, Berlin–Heidelberg–New York, 2004 ; A. K. Zvonkin, S. K. Lando, Grafy na poverkhnostyakh i ikh prilozheniya, Izd-vo MTsNMO, M., 2010 | MR | Zbl

[12] C. H. Li, J. Širáň, “Regular maps whose groups do not act faithfully on vertices, edges, or faces”, European J. Combin., 26 (2005), 521–541 | DOI | MR | Zbl

[13] R. C. Lyndon, P. E. Schupp, Combinatorial Group Theory, Springer, Berlin–Heidelberg–New York, 1977 ; R. Lindon, P. Shupp, Kombinatornaya teoriya grupp, Mir, M., 1980 | MR | Zbl | MR

[14] G. Malle, J. Saxl, T. Weigel, “Generation of classical groups”, Geom. Dedicata, 49 (1994), 85–116 | DOI | MR | Zbl

[15] B. H. Neumann, “Some remarks on infinite groups”, J. London Math. Soc., 12 (1937), 120–127 | Zbl

[16] J. Širáň, “Regular maps on a given surface: a survey”, Topics in Discrete Mathematics, Algorithms Combin., 26, Springer, Berlin, 2006, 591–609 | MR | Zbl

[17] J. Širáň, T. W. Tucker, “Symmetric maps”, Topics in Topological Graph Theory, Encyclopedia Math. Appl., 128, Cambridge Univ. Press, Cambridge, 2009, 199–224 | MR | Zbl

[18] J. Širáň, T. W. Tucker, M. E. Watkins, “Realizing finite edge-transitive orientable maps”, J. Graph Theory, 37 (2001), 1–34 | DOI | MR | Zbl

[19] T. R. S. Walsh, “Hypermaps versus bipartite maps”, J. Combin. Theory Ser. B, 18 (1975), 155–163 | DOI | MR | Zbl