Wrappings of permutations

Author:
Saul Stahl

Journal:
Trans. Amer. Math. Soc. **300** (1987), 133-152

MSC:
Primary 20F05

DOI:
https://doi.org/10.1090/S0002-9947-1987-0871668-9

MathSciNet review:
871668

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Abstract: A theory of wrappings of permutations is constructed which is analogous to the well-known concept of branched coverings of Riemann surfaces. It is shown that this theory is strong enough to contain combinatorial definitions of such well-known groups as Fuchsian groups of the first kind and triangle groups.

**[1]**J. L. Brenner and R. C. Lyndon,*Orbits of the product of two permutations*, European J. Combin.**4**(1983), 279-293. MR**743150 (85c:20003)****[2]**R. Cori, A. Machi, L. G. Penaud and B. Vauquelin,*On the automorphism group of a planar hypermap*, European J. Combin.**2**(1981), 331-334. MR**638407 (83e:05059)****[3]**R. C. Lyndon and P. E. Schupp,*Combinatorial group theory*, Ergeb. Math. Grenzgeb. (3)**89**(1977). MR**0577064 (58:28182)****[4]**A. Machi,*Homology of hypermaps*, J. London Math. Soc. (2)**31**(1985), 10-16. MR**810557 (87d:05067)****[5]**W. Magnus,*Noneuclidean tesselations and their groups*, Academic Press, New York, 1974. MR**0352287 (50:4774)****[6]**G. A. Miller,*On the product of two substitutions*, Amer. J. Math.**22**(1900), 185-190. MR**1505829****[7]**M. H. A. Newman,*Elements of the topology of plane sets of points*, Cambridge University Press, New York, 1961. MR**0132534 (24:A2374)****[8]**H. Poincaré,*Théorie des groupes Fuchsiennes*, Acta Math.**1**(1982), 1-62.**[9]**H. Seifert and W. Threlfall,*A textbook of topology*, Academic Press, New York, 1980. MR**575168 (82b:55001)****[10]**S. Stahl,*A combinatorial analog of the Jordan Curve Theorem*, J. Combin. Theory (B)**35**(1983), 28-38. MR**723568 (85e:05065)****[11]**-,*The average genus of classes of graph embeddings*, Congr. Numer.**40**(1983), 375-388. MR**734384 (85d:05106)****[12]**D. W. Walkup,*How many ways can a permutation be factored into two*-*cycles*? Discrete Math.**28**(1979), 315-319. MR**548630 (81d:05005)****[13]**A. T. White,*Graphs, groups and surfaces*, North-Holland Mathematical Studies 8, North-Holland, Amsterdam, 1984. MR**780555 (86d:05047)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1987-0871668-9

Article copyright:
© Copyright 1987
American Mathematical Society