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Classifying Descents According to Parity
Sergey Kitaev1 and Jeffrey Remmel2
1Institute of Mathematics, Reykjavík University, IS-103 Reykjavík, Iceland
sergey@ru.is
2Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA
remmel@math.ucsd.edu
Annals of Combinatorics 11 (2) p.173-193 June, 2007
AMS Subject Classification: 05A15
Abstract:
In this paper we refine the well-known permutation statistic “descent” by fixing parity of (exactly) one of the descent's numbers. We provide explicit formulas for the distribution of these (four) new statistics. We use certain differential operators to obtain the formulas. Moreover, we discuss connection of our new statistics to the Genocchi numbers. We also provide bijective proofs of some of our results.
Keywords: permutation statistics, descents, parity, distribution, bijection

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