Geodesic
Classifying descents according to equivalence \(\operatorname{mod} k\)
The electronic journal of combinatorics, Tome 13 (2006)
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In an earlier paper the authors refine the well-known permutation statistic "descent" by fixing parity of (exactly) one of the descent's numbers. In the current paper, we generalize the results of that earlier paper by studying descents according to whether the first or the second element in a descent pair is divisible by $k$ for some $k\geq 2$. 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 and state a number of open problems.
DOI : 10.37236/1090
Classification : 05A15, 05E05
Mots-clés : permutation statistic, distribution 
@article{10_37236_1090,
     author = {Sergey Kitaev and Jeffrey Remmel},
     title = {Classifying descents according to equivalence \(\operatorname{mod} k\)},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1090},
     zbl = {1097.05003},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1090/}
}
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Sergey Kitaev; Jeffrey Remmel. Classifying descents according to equivalence \(\operatorname{mod} k\). The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1090

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