The Euler-Mahonian distributions over the words. (Les distributions euler-mahoniennes sur les mots.) (French) Zbl 0829.05058

Author’s abstract: The purpose of this paper is to calculate the Euler- Mahonian distribution over each rearrangement class \(R(c)\) of a given word. After updating MacMahon’s calculation of this distribution, it is shown that the Schur function algebra gives all the necessary ingredients for deriving this distribution. Furthermore, this approach provides an extension to the calculation of some distributions over the colored biwords, as well as other multibasic hypergeometric extensions that have not been reproduced here.


05E05 Symmetric functions and generalizations
05E99 Algebraic combinatorics
05E10 Combinatorial aspects of representation theory
Full Text: DOI


[1] Andrews, G.E., The theory of partitions, () · Zbl 0155.09302
[2] Cartier, P.; Foata, D., Problémes combinatoires de permutations et réarrangements, () · Zbl 0186.30101
[3] R.J. Clarke, A short proof of a result of Foata and Zeilberger. Adv. Appl. Math. à paraître. · Zbl 0838.05001
[4] Denert, M., The genus zeta function of hereditary orders in central simple algebras over global fields, Math. comp., 54, 449-465, (1990) · Zbl 0687.16003
[5] Désarménien, J.; Foata, D., Fonctions symétriques et séries hypergéométriques basiques multivarićes, Bull. soc. math. France, 113, 3-22, (1985) · Zbl 0644.05005
[6] Désarménien, J.; Foata, D., Fonctions symétriques et séries hypergéométriques basiques multivariées, II, combinatoire énumérative, (), 68-90
[7] Désarménien, J.; Foata, D., Statistiques d’ordre sur LES permutations colorées, Discrete math., 87, 133-148, (1991) · Zbl 0742.05082
[8] Foata, D., On the netto inversion number of a sequence, (), 236-240 · Zbl 0157.03403
[9] Foata, D.; Zeilberger, D., Denert’s permutation statistic is indeed Euler-Mahonian, Stud. appl. math., 83, 31-59, (1990) · Zbl 0738.05001
[10] Gasper, G.; Rahman, M., Basic hypergeometric series, (), 35
[11] Garsia, A.M.; Gessel, I., Permutation statistics and partitions, Adv. math., 31, 288-305, (1979) · Zbl 0431.05007
[12] Gessel, I., Generating functions and enumeration of sequences, ()
[13] Han, G.-N., Une transformation fondamentale sur LES réarrangements de mots, Adv. math., 105, 26-41, (1994) · Zbl 0798.05001
[14] Knuth, D.E., Permutations, matrices, and generalized Young tableaux, Pacific J. math., 34, 709-727, (1970) · Zbl 0199.31901
[15] Knuth, D.E., The art of computer programming, () · Zbl 0191.17903
[16] Macdonald, I.G., Symmetric functions and Hall polynomials, (1979), Clarendon Press Oxford · Zbl 0487.20007
[17] MacMahon, P.A., The indices of permutations and the derivation therefrom of functions of a single variable associated with the permutations of any assemblage of objects, Amer. J. math., 35, 314-321, (1913) · JFM 44.0076.02
[18] MacMahon, P.A., (), réimprimé par Chelsea, New York, 1955)
[19] Rawlings, D., Permutation and multipermutation statistics, (), P-23
[20] Rawlings, D., Generalized worpitzky identities with applications to permutation enumeration, European J. combin., 2, 67-78, (1981) · Zbl 0471.05006
[21] Remmel, J.B., Permutation statistics and (k, l)-hook Schur functions, Discrete math., 67, 271-298, (1987) · Zbl 0666.05002
[22] V. Reiner, Commutation orale, 1992.
[23] Stanley, R.P., Ordered structures and partitions, (), 119
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.