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Classifying Descents According to Parity

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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.

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Authors and Affiliations

  1. Institute of Mathematics, Reykjavík University, IS-103, Reykjavík, Iceland

    Sergey Kitaev

  2. Department of Mathematics, University of California, San Diego, La Jolla, CA, 92093-0112, USA

    Jeffrey Remmel

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  1. Sergey Kitaev
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  2. Jeffrey Remmel
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Correspondence to Sergey Kitaev.

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Received September 7, 2005

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Kitaev, S., Remmel, J. Classifying Descents According to Parity. Ann. Comb. 11, 173–193 (2007). https://doi.org/10.1007/s00026-007-0313-2

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  • DOI: https://doi.org/10.1007/s00026-007-0313-2

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