# Counting permutations by runs

```@article{Zhuang2016CountingPB,
title={Counting permutations by runs},
author={Yan Zhuang},
journal={J. Comb. Theory, Ser. A},
year={2016},
volume={142},
pages={147-176}
}```
• Yan Zhuang
• Published 9 May 2015
• Mathematics
• J. Comb. Theory, Ser. A
28 Citations
Hopping from Chebyshev Polynomials to Permutation Statistics
• Mathematics
Electron. J. Comb.
• 2019
We prove various formulas which express exponential generating functions counting permutations by the peak number, valley number, double ascent number, and double descent number statistics in terms
Reciprocals of exponential polynomials and permutation enumeration
We show that the reciprocal of a partial sum with 2m terms of the alternating exponential series is the exponential generating function for permutations in which every increasing run has length
The alternating run polynomials of permutations
• Mathematics
• 2019
In this paper, we first consider a generalization of the David-Barton identity which relate the alternating run polynomials to Eulerian polynomials. By using context-free grammars, we then present a
Shuffle-compatible permutation statistics
• Mathematics
• 2018
C O ] 2 0 A ug 2 02 0 Plethystic formulas for permutation enumeration
• Mathematics
• 2020
We prove several general formulas for the distributions of various permutation statistics over any set of permutations whose quasisymmetric generating function is a symmetric function. Our formulas
Alternating runs of permutations and the central factorial numbers
• Mathematics
• 2022
Let R(n, k) be the number of permutations of {1, 2, . . . , n} with k alternating runs. In this paper, we establish the relationships between R(n, k) and the central factorial numbers of even indices
Fe b 20 21 REFINED EULERIAN NUMBERS AND BALLOT PERMUTATIONS
• Mathematics
• 2021
Abstract. A ballot permutation is a permutation π such that in any prefix of π the descent number is not more than the ascent number. In this article, we obtained a formula in close form for the

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Electron. J. Comb.
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Electron. J. Comb.
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