Permutations selon leurs pics, creux, doubles montees et double descentes, nombres d’Euler et nombres de Genocchi. (French) Zbl 0409.05003


05A05 Permutations, words, matrices
11A55 Continued fractions
05A15 Exact enumeration problems, generating functions
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
Full Text: DOI


[1] André, D., Developpements de sec \(x\) et de tan \(x\), C.R. Acad. Sc. Paris, 88, 965-967 (1879) · JFM 11.0187.01
[2] André, D., Sur les permutations alternées, J. Math. Pur. Appl., 7, 167-184 (1881) · JFM 13.0152.02
[3] Carlitz, L., A conjecture concerning Genocchi numbers, K. norske Vidensk. Selsk. Sk., 9, 1-4 (1972)
[4] Carlitz, L., Permutations with a prescribed pattern, Math. Nachr., 58, 31-53 (1973) · Zbl 0229.05015
[5] Comtet, L., (Analyse combinatoire, Vol. 1 (1970), Presses Universitaires de France: Presses Universitaires de France Paris) · Zbl 0221.05001
[6] Dumont, D., Interprétations combinatoires des nombres de Genocchi, Duke Math. J., 41, 305-318 (1974) · Zbl 0297.05004
[7] Dumont, D., Une nouvelle interprétation combinatoire des nombres tangents,, (5-th Hungarian Conference on Combinatorics. 5-th Hungarian Conference on Combinatorics, Keszthely (1976)), à paraitre
[8] D. Dumont, communication personnelle.; D. Dumont, communication personnelle.
[9] D. Dumont et G. Viennot, Interprétation combinatoire de la génération de Seidel des nombres de Genocchi, à paraître.; D. Dumont et G. Viennot, Interprétation combinatoire de la génération de Seidel des nombres de Genocchi, à paraître.
[10] Flajolet, P., Analyse d’algorithmes de manipulation de tichiers, (Rapport Laboria No. 321 (1973), IRIA: IRIA Rocquencourt)
[11] P. Flajolet, Combinatorial aspects of continued fractions, à paraître.; P. Flajolet, Combinatorial aspects of continued fractions, à paraître. · Zbl 0445.05015
[12] Foate, D.; Schützenberger, M. P., Théorie géométrique des polynómes culériens, (Lecture Notes in Math. (1970), Springer Verlag: Springer Verlag Berlin), No. 138 · Zbl 0214.26202
[13] Foata, D.; Schützenberger, M. P., Nombres d’Euler et permutations alternantes, (A Survey of Combinatorial Theory (1973), North-Holland: North-Holland Amsterdam), 173-187 · Zbl 0271.05005
[14] Foata, D.; Strehl, V., Rearrangements of the symmetric group and enumerative properties of the tangent and secant numbers, Math. Z., 197, 257-264 (1974) · Zbl 0274.05007
[15] Françon, J., Histoires de fichiers, RAIRO Inf. Th., 12, 49-62 (1978) · Zbl 0377.68034
[16] Foulkes, H. O., Enumeration of permutations with prescribed up-down and inversion sequences, Discrete Math., 15, 235-252 (1976) · Zbl 0338.05002
[17] Gandhi, J. M., A conjectured representation of Genocchi numbers, Amer. Math. Monthly, 77, 502-506 (1970) · Zbl 0198.37003
[18] Knuth, D. E., (The Art of Computer Programming, Vol. 1 (1973), Addison-Wesley: Addison-Wesley Reading, MA) · Zbl 0302.68010
[19] Macmahon, P. A., Combinatorial Analysis (1960), Chelsea: Chelsea New York, réimpression · JFM 31.0219.01
[20] Niven, I., A combinatorial problem of finite sequences, Nieuw Archief voor Wiskunde, 16, 116-123 (1968) · Zbl 0164.33102
[21] Riordan, J.; Stein, P. R., Proof of a conjecture on Genocchi numbers, Discrete Math., 5, 381-388 (1973) · Zbl 0271.05004
[22] Rosen, J., The number of product-weighted lead codes for ballots and its relation to the Ursell function of the linear Ising model, J.C.T. Serie A, 20, 377-384 (1976) · Zbl 0339.05009
[23] Seidel, L., Über eine einfache Entstehungweise der Bernoullischen Zahlen und einiger verwandten Reihen, Sitzungsberichte der Münchener Akademie, Math. Phys. Klasse, 157-187 (1877)
[24] Strehl, V., Enumeration of alternating permutations according to peak sets, J.C.T. Serie A, 24, 238-240 (1978) · Zbl 0373.05005
[25] Touchard, J., Sur certaines équations fonctionnelles, (Proc. Int. Math. Congress, Toronto, Vol. 1 (1924)), 465, 1928 · JFM 54.0440.03
[26] G. Viennot Permutations selon leur forme, à paraître.; G. Viennot Permutations selon leur forme, à paraître.
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