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Proceedings of the American Mathematical Society

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On $ q$-derangement numbers

Author: Michelle L. Wachs
Journal: Proc. Amer. Math. Soc. 106 (1989), 273-278
MSC: Primary 05A15; Secondary 05A30
MathSciNet review: 937015
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Abstract: We derive a $ q$-analogue of the classical formula for the number of derangements of an $ n$ element set. Our derivation is entirely analogous to the classical derivation, but relies on a descent set preserving bijection between the set of permutations with a given derangement part and the set of shuffles of two permutations.

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  • [A] M. Aigner, Combinatorial theory, Springer-Verlag, New York, 1979. MR 542445 (80h:05002)
  • [BW] A. Björner and M. Wachs, $ q$-Hook length formulas for forests, J. Combin. Th. Ser A (to appear).
  • [D$ _{1}$] J. Désarménien, Une autre interprétation du nombre de dérangements, Actes $ {8^e}$ Séminaire Lotharingien de Combinatoire, I.R.M.A. Strasbourg, 1984, pp. 11-16.
  • [D$ _{2}$] J. Désarménien, personal communication.
  • [G] I. Gessel, Counting permutations by descents, greater index, and cycle structure, unpublished work.
  • [GG] A. M. Garsia and I. Gessel, Permutation statistics and partitions, Adv. in Math. 31 (1979), 288-305. MR 532836 (80e:05013)
  • [GR] A. M. Garsia and J. Remmel, A combinatorial interpretation of $ q$-derangement and $ q$-Laguerre numbers, European J. Combin. 1 (1980), 47-59. MR 576766 (81g:05011)
  • [M] P. A. MacMahon, The indices of permutations and the derivation therefrom of functions of a single variable associated with permutations of any assemblage of objects, Amer. J. Math. 35 (1913), 281-322; reprinted in Percy Alexander MacMahon: Collected papers, vol. 1 (G. E. Andrews, ed.), M.I.T. Press, Cambridge MA., 1978, pp. 508-549. MR 1506186
  • [DW] J. Désarménien and M. Wachs, Descentes des dérangements et mots circulaires, Actes 19 Séminaire Lotharinjien de Combinatoire, I.R.M.A. Strasbourg, 1988, 13-21.

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