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Graphical Major Indices (1995) [7 citations — 1 self]

by Dominique Foata ,  Doron Zeilberger
II, Sém. Lothar. Combin
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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.

Citations

1516 The Art of Computer Programming – Knuth - 1968
353 in ‘‘Algebraic Combinatorics on Words – Lothaire
324 The encyclopedia of integer sequences – Sloane, Plouffe - 1995
295 The theory of partitions – Andrews - 1998
224 Basic hypergeometric series – Gasper, Rahman - 1990
36 On the Netto inversion number of a sequence – Foata - 1968
23 Eulerian calculus, II: an extension of Han's fundamental transformation – Clarke, Foata - 1995
20 Permutation statistics of indexed permutations – Steingrimsson - 1994
19 La série génératrice exponentielle dans les problèmes d’énumération, LesPresses de l’Université deMontréal – Foata - 1974
17 Eulerian Calculus, III: The Ubiquitous Cauchy Formula – Clarke, Foata - 1995
12 Convolution polynomials – Knuth - 1992
12 The indices of permutations and the derivation therefrom of functions of a single variable associated with the permutations of any assemblage of objects – MacMahon - 1913
9 Th'eorie des esp `eces et combinatoire des structures arborescentes." Montr'eal, Universit 'e du Qu'ebec `a Montr'eal, Publ – Bergeron, Labelle, et al. - 1994
6 Combinatory Analysis, vol. 1 – MacMahon - 1915
4 distributions Euler-Mahoniennes sur les mots, Discrete Math – Foata, Les - 1995
2 Ordres bipartitionnaires et statistiques sur les mots – Han - 1995
1 and Dominique Foata, "Eulerian Calculus, I: univariable statistics – Clarke - 1994
1 Analyse Combinatoire, vol. 1 and 2." Paris, Presses Universitaires de Frances – Comtet - 1970
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