Graphical major indices

Journal of Computational and Applied Mathematics

Volumn 68, Issue 1-2, 1996, Pages 79-101

  Foata, Dominique ^a   Zeilberger, Doron ^b  

^a UNIVERSITÉ DE STRASBOURG   (France)

^b Temple University   (United States)

Author keywords

Bipartitional relation; MacMahon Verfahren; Major index

Indexed keywords

GRAPH THEORY; INVERSE PROBLEMS; NUMBER THEORY; OPTIMIZATION;

ARBITRARY GRAPHS; BIPARTITIONAL RELATION; CLASSICAL STATISTICS; MACMAHON VERFAHREN; MAJOR INDEX; NUMBER OF INVERSIONS; PERMUTATION;

STATISTICAL METHODS;

EID: 0030123572     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/0377-0427(95)00254-5     Document Type: Article

References (20)

1. G.E. Andrews, The Theory of Partitions (Addison-Wesley, London, 1976) (Encyclopedia of Math. and its Appl., Vol. 2).
2. F. Bergeron, G. Labelle and P. Leroux, Théorie des espèces et combinatoire des structures arborescentes, Université du Québec à Montréal, Montréal, Publ. du LACIM, No. 19, 1994.
3. R.J. Clarke and D. Foata, Eulerian calculus, I: univariable statistics, European J. Combin. 15 (1994) 345-362.
4. R.J. Clarke and D. Foata, Eulerian calculus, II: an extension of Han's fundamental transformation, European J. Combin. 16 (1995) 221-252.
5. R.J. Clarke and D. Foata, Eulerian calculus, III: the ubiquitous Cauchy formula, European J. Combin. 16 (1995) 329-355.
6. L. Comtet, Analyse Combinatoire, Vols. 1 and 2 (Presses Universitaires de Frances, Paris, 1970) (English edition: Advanced Combinatorics, Reidel, Dordrecht, 1974).
7. D. Foata, On the Netto inversion number of a sequence, Proc. Amer. Math. Soc. 19 (1968) 236-240.
8. D. Foata, La Série Génératrice Exponentielle dans les Problèmes d'Énumération (Presses Universitaires de Montréal, Montréal, 1974).
9. D. Foata, Les distributions Euler-Mahoniennes sur les mots, Discrete Math. 139 (1995) 167-187.
10. G. Gasper and M. Rahman, Basic Hypergeometric Series (Cambridge Univ. Press, London, 1990) (Encyclopedia of Math. and its Appl., Vol. 35).
11. G.-N. Han, Ordres bipartitionnaires et statistiques sur les mots, Electronic J. Combin., to appear.
12. G.-N. Han, Une démonstration "vérificative" d'un résultat de Foata-Zeilberger sur les relations bipartitionnaires, J. Comput. Appl. Math. 68 (1996) 159-162 (this volume).
13. D.E. Knuth, The Art of Computer Programming, Vol. 3, Sorting and Searching (Addison-Wesley, Reading, MA, 1973).
14. D.E. Knuth, Convolutional polynomials, Mathematica J. 2 (1992) 67-78.
15. M. Lothaire, Combinatorics on Words (Addison-Wesley, Reading, MA, 1983) (Encyclopedia of Math. and its Appl., Vol. 17).
16. P.A. MacMahon, 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 (1913) 314-321.
17. P.A. MacMahon, Combinatory Analysis, Vol. 1 (Cambridge Univ. Press, Cambridge, 1915) (Reprinted by Chelsea, New York, 1955).
18. P.A. MacMahon, Collected Papers, Vol. 1 (MIT Press, Cambridge, MA, 1978).
19. N.J.A. Sloane, A Handbook of Integer Sequences (Academic Press, New York, 1973).
20. E. Steingrimsson, Permutation statistics of indexed permutations, European J. Combin. 15 (1994) 187-205.