Indecomposable permutations, hypermaps and labeled Dyck paths

Journal of Combinatorial Theory. Series A

Volumn 116, Issue 8, 2009, Pages 1326-1343

  Cori, Robert ^a  

^a UNIVERSITÉ DE BORDEAUX   (France)

Author keywords

Bijective proofs; Combinatorial maps; Dyck paths; Enumeration; Permutations; Stirling numbers

Indexed keywords

EID: 70349329526     PISSN: 00973165     EISSN: 10960899     Source Type: Journal    
DOI: 10.1016/j.jcta.2009.02.008     Document Type: Article

References (29)

1. Aguiar M., and Sottile F. Structure of the Malvenuto-Reutenauer Hopf algebra of permutations. Adv. Math. 191 (2004) 225-275
2. Arques D., and Béraud J.-F. Rooted maps on orientable surfaces, Riccati's equation and continued fractions. Discrete Math. 215 (2000) 1-12
3. n. C. R. Acad. Sci. Paris Ser. A 275 (1972) 569-572
4. Cori R. Un code pour les graphes planaires ses applications. Astérisque 27 (1975) 1-169
5. Cori R., and Machí A. Maps hypermaps and their automorphisms, a survey. Expo. Math. 10 (1992) 403-467
6. Cvitanovic P., Lautrup B., and Pearson R.B. Number and weights of Feynman diagrams. Phys. Rev. D 18 (1978) 1939-1949
7. Ossona de Mendez P., and Rosenstiehl P. Transitivity and connectivity of permutations. Combinatorica 24 (2004) 487-502
8. Ossona de Mendez P., and Rosenstiehl P. Encoding pointed maps by double occurrence words. KAM-DIMATIA Ser. 752 (2005) 487-502
9. P. Deleham, Delta operator, in: On-Line Encyclopedia of Integer Sequences, A084938, 2003
10. Dixon J.D. Asymptotics of generating the symmetric and alternating groups. Electron. J. Combin. 12 (2005) R56
11. Drake D. The combinatorics of associated Hermite polynomials. European J. Combin. 30 (2009) 1005-1021
12. Duchamp G., Hivert F., and Thibon J.-Y. Noncommutative symmetric functions VI: Free quasi-symmetric functions and related algebras. Internat. J. Algebra Comput. 12 (2002) 671-717
13. Edmonds J.R. A combinatorial representation for polyhedral surfaces. Notices Amer. Math. Soc. 7 (1960) 646
14. Foata D., and Schützenberger M.P. Théorie géométrique des polyômes Eulériens. Lecture Notes in Math. (1970), Springer, Paris
15. Gonthier G. A computer checked proof of the four colour theorem (2005). http://research.microsoft.com/~gonthier/4colproof.pdf
16. Heffter L. Über das Problem der Nachbargebiete. Math. Ann. 38 (1891) 477-508
17. Jacques A. Sur le genre d'une paire de substitutions. C. R. Acad. Sci. Paris 267 (1968) 625-627
18. Jones G., and Singerman D. Theory of maps on orientable surfaces. Proc. London Math. Soc. 31 (1978) 211-256
19. A. Lentin, Contribution à une théorie des equations dans les monoïdes libres, PhD thesis, Faculté des Sciences, Université de Paris, 1969
20. Machí A. The Riemann-Hurwitz formula for the centralizer of a pair of permutations. Arch. Mat. 42 (1984) 280-288
21. Mohar B., and Thomassen C. Graphs on surfaces (2001), John Hopkins Univ. Press
22. Roblet E., and Viennot X.G. Théorie combinatoire des T-fractions approximants de Padé en deux points. Discrete Math. 153 (1996) 271-288
23. Rotman J.J. An Introduction to the Theory of Groups (1999), Springer
24. Stanley R.P. Enumerative Combinatorics, vol. 2 (1999), Cambridge Univ. Press
25. Tutte W.T. A census of planar maps. Canad. J. Math. 15 (1963) 249-271
26. Tutte W.T. What is a map?. New Directions in the Theory of Graphs (1973), Academic Press, New York 309-325
27. Walsh T.R.S. Hypermaps versus bipartite maps. J. Combin. Theory Ser. B 18 (1975) 155-163
28. Walsh T.R.S., and Lehman A.B. Counting rooted maps by genus I. J. Combin. Theory Ser. 13 (1972) 192-218
29. Youngs J. Minimal embeddings the genus of a graph. J. Math. Mech. 12 (1963) 303-315