Classifying Descents According to Parity
نویسندگان
چکیده
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.
منابع مشابه
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In [5] the authors refine the well-known permutation statistic “descent” by fixing parity of (exactly) one of the descent’s numbers. In this paper, we generalize the results of [5] by studying descents according to whether the first or the second element in a descent pair is equivalent to k mod k ≥ 2. We provide either an explicit or an inclusion-exclusion type formula for the distribution of t...
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