A cycle lemma for permutation inversions

Discrete Mathematics

Volumn 257, Issue 1, 2002, Pages 1-13

  Brunetti, S ^a,b   Del Lungo, A ^a   Del Ristoro, F ^a  

^a UNIVERSITY OF SIENA   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Congruence; Cyclic shift; Gaussian binomial coefficient; Greatest common divisor; Inversion; Major; Multiset; Permutation

Indexed keywords

EID: 31244432354     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(02)00254-6     Document Type: Article

References (13)

1. G.E. Andrews, The Theory of Partitions, in: G.C. Rota (Ed.), Encyclopedia of Mathematics and its -Applications, Vol. 2, Addison-Wesley, Reading, MA, 1976.
2. M.D. Atkinson, J.R. Sack, Generating binary trees at random, Inform. Proc. Lett. 41 (1992) 21-23.
3. J. Bonin, L. Shapiro, R. Simion, Some q-analogues of the Schröder numbers arising from combinatorial statistics on lattice paths, J. Statist. Plann. Inference 34 (1993) 35-55.
4. K.L. Chung, W. Feller, Fluctuations in coin-tossing, Proc. Natl. Acad. Sci. USA 35 (1968) 605-608.
5. N. Dershowitz, S. Zaks, The cycle lemma and some applications, Eur. J. Combin. 11 (1990) 35-40.
6. D. Fbata, On the Netto Inversion number of a sequence, Proc. Amer. Math. Soc. 19 (1968) 236-240.
7. A.M. Garsia, I. Gessel, Permutation statistics and partitions, Adv. Math. 31 (1979) 288-305.
8. R.L. Graham, D.E. Knuth, O. Patashnik, Concrete Mathematics, 2nd Edition, Addison-Wesley, Reading, MA, 1994.
9. G.H. Hardy, E.M. Wright, An Introduction to the Theory of Numbers, 4th Edition, Oxford University Press, London, 1965.
10. P.A. MacMahon, Combinatorial Analysis, Vol. 2, Cambridge University Press, New York, 1916.
11. T.V. Narayana, Cyclic permutation of lattice paths and the Chung-Feller theorem, Skand. Acuarietidskritt (1967) 23-30.
12. G.M. Raney, Functional composition patterns and power series reversion, Trans. Amer. Math. Soc. 94 (1960) 441-451.
13. R. Stanley, Enumerative Combinatorics, Vol. 1, Wadsworth, Belmont, CA, 1986.