Cardinality of Rauzy classes
- [1] Institut de Mathématiques de Luminy (UMR 6206) Campus de Luminy, Case 907 13288 MARSEILLE Cedex 9
Annales de l’institut Fourier (2013)
- Volume: 63, Issue: 5, page 1651-1715
- ISSN: 0373-0956
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top- L. Ahlfors, Lectures on quasiconformal mappings, (1966), Van Nostrand Zbl0138.06002MR200442
- A. Avila, G. Forni, Weak mixing for interval exchange transformations and translation flows, Ann. of Math. 165 (2007), 637-664 Zbl1136.37003MR2299743
- G. Boccara, Nombre de representations d’une permutation comme produit de deux cycles de longueurs donnees, Discrete Math. 29 (1980), 105-13 Zbl0444.20003MR558612
- C. Boissy, Classification of Rauzy classes in the moduli space of quadratic differentials, (2009) Zbl1268.37039
- C. Boissy, Labeled Rauzy classes and framed translation surfaces, (2010) Zbl1332.37030
- A. I. Bufetov, Decay of correlations for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations and the central limit theorem for the Teichmüller flow on the moduli space of Abelian differential, J. Amer. Math. Soc 19 (2006), 579-623 Zbl1100.37002MR2220100
- G. Chapuy, Combinatoire bijective des cartes de genre supérieur, (2009)
- The Sage-Combinat community, Sage-Combinat: enhancing Sage as a toolbox for computer exploration in algebraic combinatorics, (2008)
- L. Comtet, Sur les coefficients de l’inverse de la sèrie formelle , C. R. Acad. Sci. Paris 275 (1972), 569-572 Zbl0246.05003MR302457
- A. Eskin, H. Masur, A. Zorich, Moduli spaces of Abelian differentials: the principal boundary, counting problems and the Siegel-Veech constants, Publ. Math. Inst. Hautes Études Sci. 97 (2003), 61-179 Zbl1037.32013MR2010740
- A. Eskin, A. Okounkov, Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials, Invent. Math. 145 (2001), 59-103 Zbl1019.32014MR1839286
- A. Eskin, A. Okounkov, R. Pandharipande, The theta characteristic of a branched covering, Adv. Math. 217 (2008), 873-888 Zbl1157.14014MR2383889
- P. Flajolet, R. Sedgewick, Analytic Combinatorics, (2009), Cambridge University Press Zbl1165.05001MR2483235
- A. Goupil, G. Schaeffer, Factoring n-cycles and counting maps of given genus, European J. Combin. 19 (1998), 819-834 Zbl0915.05007MR1649966
- A. Hatcher, Algebraic topology, (2002), Cambridge University Press Zbl1044.55001MR1867354
- J. H. Hubbard, Teichmüller theory and Applications to geometry, topology and dynamics. Volume 1, (2006), Matrix Editions Zbl1102.30001MR2245223
- Y. Imayoshi, M. Taniguchi, An introduction to Teichmüller spaces, (1992), Springer Zbl0754.30001MR1215481
- D. Johnson, Spin structures and quadratic forms on surfaces, J. London. Math. Soc. 22 (1980), 365-373 Zbl0454.57011MR588283
- M. Keane, Interval exchange transformations, Math. Z. 141 (1975), 77-102 Zbl0278.28010MR357739
- S. P. Kerckhoff, Simplicial systems for interval exchange maps and measured foliations, Ergodic Theory and Dynamical Systems 5 (1985), 257-271 Zbl0597.58024MR796753
- A. King, Generating indecomposable permutations, Discrete Math. 306 (2006), 508-518 Zbl1086.05004MR2212519
- M. Kontsevich, A. Zorich, Connected components of the moduli spaces of Abelian differentials wit prescribed singularities, Invent. math. 153 (2003), 631-678 Zbl1087.32010MR2000471
- S. Lando, A. Zvonkin, Graphs on Surfaces and their Applications, 141 (2004), Springer Zbl1040.05001MR2036721
- E. Lanneau, Connected components of the strata of the moduli spaces of quadratic differentials, Ann. Sci. Éc. Norm. Supér. 41 (2008), 1-56 Zbl1161.30033MR2423309
- S. Marmi, P. Moussa, J.-C. Yoccoz, The cohomological equation for Roth type interval exchange transformations, Journal of the Amer. Math. Soc. 18 (2005), 823-872 Zbl1112.37002MR2163864
- H. Masur, Interval exchange transformations and measured foliations, Ann. of Math. 115 (1982), 169-200 Zbl0497.28012MR644018
- S. Nag, The complex analytic theory of Teichmüller spaces, (1988), Wiley-Intersciences Zbl0667.30040MR927291
- A. Nogueira, D. Rudolph, Topological weak-mixing of interval exchange maps, Ergodic theory Dynam. Systems 17 (1997), 1183-1209 Zbl0958.37010MR1477038
- G. Rauzy, Echanges d’intervalles et transformations induites, Acta Arith. 34 (1979), 315-328 Zbl0414.28018MR543205
- J.-P. Serre, Topics in Galois Theory, (1992), Jones and Bartlette Publishers Zbl0746.12001MR1162313
- R. Stanley, Factorization of permutations into n-cycles, Discrete Math. 37 (1981), 255-262 Zbl0467.20005MR676430
- W. Stein, Sage Mathematics Software (Version 4.5.2), (2009)
- W. A. Veech, Gauss measures for transformations on the space of interval exchange maps, Ann. of Math. 115 (1982), 201-24 Zbl0486.28014MR644019
- W. A. Veech, Moduli space of quadratic differentials, J. d’Analyse Math. 55 (1990), 117-171 Zbl0722.30032MR1094714
- W. A. Veech, Flat surfaces, Amer. J. of Math. 115 (1993), 589-689 Zbl0803.30037MR1221838
- M. Viana, Dynamics of interval exchange maps and Teichmüller flows, (2008)
- D. Walkup, How many ways can a permutation be factored into two n-cycles?, Discrete Math. 28 (1979), 315-319 Zbl0429.05006MR548630
- J.-C. Yoccoz, Echanges d’intervalles, (2005)
- J.-C. Yoccoz, Continued fraction algorithms for interval exchange maps: an introduction, Frontiers in number theory, physics and geometry. I (2006), 401-435, Springer Zbl1127.28011MR2261103
- D. B. Zagier, J. L. Harer, The Euler characteristic of the moduli space of curves, Invent. Math. 85 (1986), 457-486 Zbl0616.14017MR848681
- A. Zorich, Flat surfaces, Frontiers in Number Theory, Physics and Geometry. Volume 1: On random matrices , zeta functions and dynamical systems (2006), 437-583, Springer Zbl1129.32012MR2261104
- A. Zorich, Explicit Jenkins-Strebel representatives of all strata of Abelian and quadratic differentials, J. Mod. Dyn. 2 (2008), 139-185 Zbl1149.30033MR2366233