S. I. Adian, The Burnside problem and identities in groups, Ergebnisse der Mathematik und ihrer Grenzgebiete 95, 1975.
DOI : 10.1007/978-3-642-66932-3

A. Avila, S. Gouëzel, and J. Yoccoz, Exponential mixing for the Teichmüller flow, Publications Mathématiques de L'IHÉSIH´IHÉS, pp.143-211, 2006.

L. Babai, On the order of uniprimitive permutation groups On the order of doubly transitive permutation groups The probability of generating the symmetric group, The Annals of Mathematics Inventiones Mathematicae Journal of Combinatorial Theory, vol.1136, issue.65 3, pp.553-568, 1981.

H. Bechtell, Theory of Groups, 1971.

H. Behr and J. L. Mennicke, A presentation of the groups ${ m PSL}(2,,p)$, Journal canadien de math??matiques, vol.20, issue.0, pp.1432-1438, 1968.
DOI : 10.4153/CJM-1968-144-7

A. T. Benjamin, C. T. Bennett, and F. Newberger, Recounting the Odds of an Even Derangement, Mathematics Magazine, vol.78, issue.5, pp.387-390, 2005.
DOI : 10.2307/30044197

E. Bertram, Even permutations as a product of two conjugate cycles, Journal of Combinatorial Theory, Series A, vol.12, issue.3, pp.368-380, 1972.
DOI : 10.1016/0097-3165(72)90102-1

S. Bloch and A. Okounkov, The Character of the Infinite Wedge Representation, Advances in Mathematics, vol.149, issue.1, pp.1-60, 2000.
DOI : 10.1006/aima.1999.1845

J. N. Bray, M. D. Conder, C. R. Leedham-green, and E. A. O-'brien, Short presentations for alternating and symmetric groups, Transactions of the American Mathematical Society, vol.363, issue.06, pp.3277-3285, 2011.
DOI : 10.1090/S0002-9947-2011-05231-1

W. Burnside, On an unsettled question in the theory of discontinuous groups, Quarterly Journal of Pure and Applied Mathematics, vol.33, pp.230-238, 1902.

J. Peter and . Cameron, Permutation groups, 1999.

C. M. Campbell, Symmetric presentations and linear groups, Finite Groups ? Coming of, Age: Proceedings of the Canadian Mathematical Society conference Contemporary Mathematics, vol.45, issue.8, pp.33-39, 1982.

C. M. Campbell and P. P. Campbell, On the minimal length of semigroup presentations, Novi Sad Journal of Mathematics, vol.34, issue.2 8, pp.17-26, 2004.

C. M. Campbell, G. Havas, C. Ramsay, and E. F. Robertson, Abstract, LMS Journal of Computation and Mathematics, vol.22, pp.266-283, 2004.
DOI : 10.1080/00927878608823336

R. D. Carmichael, Abstract definitions of the symmetric and alternating groups and certain other permutation groups, The Quarterly Journal of Mathematics, vol.49, pp.226-270, 1923.

D. J. Collins, R. I. Grigorchuk, P. F. Kurchanov, and H. Zieschang, Combinatorial group theory and applications to geometry, 1998.

S. M. Harold, W. O. Coxeter, and . Moser, Generators and Relations for Discrete Groups, p.12, 1972.

J. Dénes, P. Erd?, and P. Turán, On some statistical properties of the alternating group of degree n, L'Enseignement mathématique 15, pp.88-99, 1969.

R. Dijkgraaf, Mirror symmetry and elliptic curves The Moduli Space of Curves, Progress in Mathematics, 1995.

J. D. Dixon, The probability of generating the symmetric group, Mathematische Zeitschrift, vol.18, issue.3, pp.199-205, 1969.
DOI : 10.1007/BF01110210

D. John, B. Dixon, and . Mortimer, Permutation groups, Graduate Texts in Mathematics, vol.163, 1996.

W. Dyck and G. Studien, Gruppentheoretische Studien, Mathematische Annalen, vol.20, issue.1, pp.1-44, 1882.
DOI : 10.1007/BF01443322

D. B. Epstein, FINITE PRESENTATIONS OF GROUPS AND 3-MANIFOLDS, The Quarterly Journal of Mathematics, vol.12, issue.1, pp.205-212, 1961.
DOI : 10.1093/qmath/12.1.205

A. Eskin, H. Masur, and M. Schmoll, Billiards in rectangles with barriers, Duke Mathematical Journal, vol.118, issue.3, pp.427-463, 2003.

M. J. Evans, Problems concerning generating sets for groups

S. Garion and A. Shalev, Commutator maps, measure preservation, and $T$-systems, Transactions of the American Mathematical Society, vol.361, issue.09, pp.4631-4651, 2009.
DOI : 10.1090/S0002-9947-09-04575-9

URL : http://arxiv.org/abs/0708.3664

R. D. Girse, The number of conjugacy classes of the alternating group, BIT, vol.15, issue.2, pp.515-517, 1980.
DOI : 10.1007/BF01933645

H. Glover and D. Sjerve, The genus of PSL 2 (q) Journal für die reine und angewandte Mathematik (Crelle's, Journal), vol.380, pp.59-86, 1987.

R. M. Guralnick, W. M. Kantor, M. Kassabov, and A. Lubotzky, Presentations of finite simple groups: A quantitative approach, Journal of the American Mathematical Society, vol.21, issue.3, pp.711-774, 2008.
DOI : 10.1090/S0894-0347-08-00590-0

E. Gutkin and C. Judge, The Geometry and Arithmetic of Translation Surfaces with Applications to Polygonal Billiards, Mathematical Research Letters, vol.3, issue.3, pp.391-403, 1996.
DOI : 10.4310/MRL.1996.v3.n3.a8

R. K. Guy, Unsolved problems in number theory, Problem Books in Mathematics, issue.10, 2004.

P. Hall, THE EULERIAN FUNCTIONS OF A GROUP, The Quarterly Journal of Mathematics, vol.7, issue.1, 1936.
DOI : 10.1093/qmath/os-7.1.134

H. Godfrey, S. Hardy, and . Ramanujan, Asymptotic formulae in combinatory analysis, Proceedings of the London Mathematical Society, pp.2-17, 1918.

F. Herrlich, Teichmüller curves defined by characteristic origamis, Contemporary Mathematics, issue.397, pp.133-144, 2006.

F. Herrlich and G. Schmithüsen, An extraordinary origami curve, Mathematische Nachrichten, vol.92, issue.2, pp.219-237, 2008.
DOI : 10.1002/mana.200510597

O. Higuchi and I. Miyamoto, The 2-generators for certain simple permutation groups of small degree, SUT Journal of Mathematics, vol.34, issue.1, pp.63-74, 1998.

O. Hölder and . Bildung-zusammengesetzter-gruppen, Bildung zusammengesetzter Gruppen, Mathematische Annalen, vol.46, issue.3, pp.321-422, 1895.
DOI : 10.1007/BF01450217

P. Hubert and T. Schmidt, An introduction to Veech surfaces, Handbook of Dynamical Systems, pp.501-526, 2006.

B. Huppert and N. Blackburn, Finite Groups III, 1982.
DOI : 10.1007/978-3-642-67997-1

H. Dale and . Husemoller, Ramified coverings of Riemann surfaces, Duke Mathematical Journal, vol.29, issue.1, pp.167-174, 1962.

I. M. Isaacs and T. Zieschang, Generating Symmetric Groups, The American Mathematical Monthly, vol.102, issue.8, pp.734-739, 1995.
DOI : 10.2307/2974644

D. L. Johnson, Presentations of groups, 2nd revised ed, 1997.

C. Jordan, Sur la limite de transitivit?? des groupes non altern??s, Bulletin de la Société mathématique de France, vol.1, pp.40-71, 1873.
DOI : 10.24033/bsmf.7

M. Hall-jr, Solution of the Burnside problem for exponent six, Illinois Journal of Mathematics, vol.2, issue.4B, pp.764-786, 1958.

K. Kremer, Invariants of complex and p-adic origami-curves, 2009.

E. Samuellelì-evre and . Royer, Orbitwise countings in H(2) and quasimodular forms, International Mathematics Research Notices, vol.3, issue.1, 2006.

F. Levi, B. L. Van-der-waerden, and ¨. Uber-eine-besondere-klasse-von-gruppen, ??ber eine besondere Klasse von Gruppen, Abhandlungen aus dem Mathematischen Seminar der Universit??t Hamburg, vol.9, issue.1, pp.154-158, 1933.
DOI : 10.1007/BF02940639

P. Lochak, ON ARITHMETIC CURVES IN THE MODULI SPACES OF CURVES, Journal of the Institute of Mathematics of Jussieu, vol.4, issue.3, pp.443-508, 2005.
DOI : 10.1017/S1474748005000101

C. Roger, P. E. Lyndon, and . Schupp, Combinatorial group theory, 1977.

W. Magnus, A. Karrass, and D. Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, 2001.

G. Malle, J. Saxl, and T. Weigel, Generation of classical groups, Geometriae Dedicata, vol.3, issue.1, pp.85-116, 1994.
DOI : 10.1007/BF01263536

B. Marggraf and ¨. , Uber primitive Gruppen mit transitiven Untergruppen geringeren Grades, Inaugural-Dissertation, pp.1892-1895

H. Masur, Interval Exchange Transformations and Measured Foliations, The Annals of Mathematics, vol.115, issue.1, pp.169-200, 1982.
DOI : 10.2307/1971341

D. J. Mccullough and M. Wanderley, Writing elements of PSL(2, q) as commutators, to appear in Communications in Algebra, 2008.

C. T. Mcmullen, Teichmüller curves in genus two: discriminant and spin, Mathematische Annalen, vol.333, 2005.

Y. Minsky and B. Weiss, Nondivergence of horocyclic flows on moduli space, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.2002, issue.552, pp.131-177, 2002.
DOI : 10.1515/crll.2002.088

M. Möller, Affine groups of flat surfaces, Preprint (https

J. Nagura, On the interval containing at least one prime number, Proceedings of the Japan Academy, vol.28, issue.4, pp.177-181, 1952.
DOI : 10.3792/pja/1195570997

E. Netto, The theory of substitutions and its applications to algebra, 1982.

. Bernhard-hermann-neumann, Groups covered by finitely many cosets, Publicationes Mathematicae Debrecen, vol.3, pp.227-242, 1954.

J. Nielsen, Die Isomorphismen der allgemeinen, unendlichen Gruppe mit zwei Erzeugenden, Mathematische Annalen, vol.78, issue.1-4, pp.385-397, 1917.
DOI : 10.1007/BF01457113

S. Petr, S. I. Novikov, and . Adjan, Infinite periodic groups i, ii, iii, Mathematics of the USSR Izvestiya, vol.2, pp.209-236, 1968.

Ø. Ore, Some remarks on commutators, Proceedings of the American Mathematical Society, pp.307-314, 1951.
DOI : 10.1090/S0002-9939-1951-0040298-4

I. Pak, What do we know about the product replacement algorithm?, Groups and Computation, III, de Gruyter, pp.301-347, 2001.

L. Pyber, On the orders of doubly transitive permutation groups, elementary estimates, Journal of Combinatorial Theory, Series A, vol.62, issue.2, pp.361-366, 1993.
DOI : 10.1016/0097-3165(93)90053-B

J. J. Rotman, An introduction to the theory of groups, Graduate Texts in Mathematics, vol.148, issue.32, 1999.
DOI : 10.1007/978-1-4612-4176-8

N. Ivan and . Sanov, Solution of Burnside's problem for n = 4, pp.166-170, 1940.

G. Schmithüsen, An Algorithm for Finding the Veech Group of an Origami, Experimental Mathematics, vol.8, issue.4, pp.459-472, 2004.
DOI : 10.1017/S0143385798117479

O. Schreier and B. L. Van-der-waerden, Die Automorphismon der projektiven Gruppen, Abhandlungen aus dem Mathematischen Seminar der Universit??t Hamburg, vol.6, issue.1, pp.303-322, 1928.
DOI : 10.1007/BF02940620

D. Stork, The Action of the Automorphism Group of F 2 Upon the A 6 - and PSL(2, 7)-Defining Subgroups of F 2, Transactions of the American Mathematical Society, vol.172, pp.111-117, 1972.
DOI : 10.2307/1996336

J. G. Sunday, Presentations of the groups ${ m SL}(2,,m)$ and ${ m PSL}(2,,m)$, Journal canadien de math??matiques, vol.24, issue.0, pp.1129-1131, 1972.
DOI : 10.4153/CJM-1972-118-x

P. William and . Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bulletin of the American Mathematical Society, vol.19, issue.12, pp.417-431, 1976.

S. Tobin, On groups with exponent 4, 1954.

A. William and . Veech, Gauss measures for transformations on the space of interval exchange maps, The Annals of Mathematics, vol.115, issue.2, pp.201-242, 1982.

Y. Vorobets, Planar structures and billiards in rational polygons: the Veech alternative, Russian Mathematical Surveys, vol.51, issue.5, pp.779-817, 1996.
DOI : 10.1070/RM1996v051n05ABEH002993

D. D. Wall, Fibonacci Series Modulo m, The American Mathematical Monthly, vol.67, issue.6, pp.525-532, 1960.
DOI : 10.2307/2309169

H. Wielandt, Finite permutation groups [53], 1964.
DOI : 10.1515/9783110863383.119

P. D. Williams, Presentations of linear groups, 1982.

H. Zieschang, Generators of the free product with amalgamation of two infinite cyclic groups, Mathematische Annalen, vol.17, issue.3, pp.195-221, 1977.
DOI : 10.1007/BF01361856

E. Thilo and . Zieschang, Primitive permutation groups containing a p-cycle, Archiv der Mathematik, vol.64, issue.6, pp.471-474, 1995.

A. Zorich and F. Surfaces, Frontiers in Number Theory, Physics, and Geometry I: On Random Matrices, Zeta Functions, and Dynamical Systems, pp.437-583, 2006.

.. Closed, 57 coset diagram 42 indegree of a vertex, 42 origamal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 realizer, p.109

A. Outdegree-of, 56 regular 56 strongly connected, p.56

.. Burnside, 105 commutator subgroup, 36 dihedral, vol.105, issue.28, pp.76-105

.. Schur-multiplier, 90 special affine 50 special linear, 27 tetrahedral, vol.36, issue.83, p.43

H. Holomorphic-1-form and .. , 25 Horizontal shear, p.39

.. Local-coordinate, 25 M Marking of an edge, p.27

O. Orbital and .. , 55 diagonal, p.55

.. Realizer, 109 Regular permutation group, p.55

V. Veech and D. , 37 Veech group dual, p.36