Classifying Descents According to Equivalence mod k

In [5] the authors refine the well-known permutation statistic "descent" by fixing parity of 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 the new statistics. Based on our results we obtain combinatorial proofs of a number of remarkable identities. We also provide bijective proofs of some of our results.

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Sergey Kitaev, Jeffrey B. Remmel
• Keywords: COMBINATORICS 2006, Descent Pair, Inclusion-exclusion Type Formula, Well-known Permutation