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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0937015-6
PII: S 0002-9939(1989)0937015-6
Article copyright: © Copyright 1989 American Mathematical Society