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Abstract: A generalization of the classical statistics "maj" and "inv" (the major index and number of inversions) on words is introduced, parameterized by arbitrary graphs on the underlying alphabet. The question of characterizing those graphs that lead to equi-distributed "inv" and "maj" is posed and answered. (Update)
Context of citations to this paper: More
.... large letters, the classical permutation statistics can be further refined to take large inequalities into account (see Clarke and Foata 1994, 1995a, 1995b) Those statistics are denoted by des k , exc k , or by des U , exc U , in Problem 10.5.2) It is also...
...correspondence. Recent work involving inversions, major indices, and permutation statistics is presented in [7, 9, 12, 30, 31, 32, 33, 34, 35, 36, 39, 40]. Proportionally speaking, w i statistics are rather scarce. For example, there are over 1662 trillion Mahonian...
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BibTeX entry: (Update)
Foata, D. and Krattenthaler, C. (1995). Graphical Major Indices, II, S'eminaire Lotharingien de Combinatoire, http://cartan.u-strasbg.fr/¸slc, B34k, 16 pp. http://citeseer.ist.psu.edu/foata95graphical.html More
@misc{ foata95graphical,
author = "D. Foata and C. Krattenthaler",
title = "Graphical Major Indices",
text = "Foata, D. and Krattenthaler, C. (1995). Graphical Major Indices, II, S'eminaire
Lotharingien de Combinatoire, http://cartan.u-strasbg.fr/¸slc, B34k, 16
pp.",
year = "1995",
url = "citeseer.ist.psu.edu/foata95graphical.html" }
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134 Basic Hypergeometric Series (context) - Gasper, Rahman - 1990
114 The Theory of Partitions (context) - Andrews - 1976
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9 La s'erie g'en'eratrice exponentielle dans les probl `emes d (context) - Foata - 1974
7 II: an extension of Han's fundamental transformation (context) - Clarke, Foata et al. - 1995
6 The indices of permutations and the derivation therefrom of .. (context) - MacMahon - 1913
6 Permutation Statistics of Indexed Permutations - Steingrimsson - 1994
5 III: the ubiquitous Cauchy formula (context) - Clarke, Foata et al. - 1995
4 Th'eorie des esp `eces et combinatoire des structures arbore.. (context) - Bergeron, Labelle et al. - 1994
4 Eulerian Calculus, I: univariable statistics (context) - Clarke, Foata - 1994
3 Ordres bipartitionnaires et statistiques sur les mots (context) - Han - 1995
3 Collected Papers (context) - MacMahon - 1978
3 Les distributions Euler-Mahoniennes sur les mots (context) - Foata - 1995
2 Convolutional Polynomials (context) - Knuth - 1992
1 Analyse Combinatoire, vol. 1 and 2 (context) - Comtet - 1974
1 Combinatory Analysis, vol. 1 (context) - MacMahon - 1955
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