Counting permutations by runs

  title={Counting permutations by runs},
  author={Yan Zhuang},
  journal={J. Comb. Theory, Ser. A},
  • Yan Zhuang
  • Published 9 May 2015
  • Mathematics
  • J. Comb. Theory, Ser. A
Plethystic formulas for permutation enumeration
Hopping from Chebyshev Polynomials to Permutation Statistics
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
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
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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
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
Eulerian polynomials and descent statistics


Combinatorics of permutations
This book discusses Permutations as Genome Rearrangements, algorithms and permutations, and the proof of the Stanley-Wilf Conjecture.
Decomposition Based Generating Functions for Sequences
Numerous combinatorial enumeration problems may be reduced to equivalent problems of enumerating sequences with prescribed restrictions. For example, the expression, given by Tutte [38], for the
Noncommutative symmetric functions
This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an
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The length is(w) of the longest increasing subsequence of a permutation w in the symmetric group Sn has been the object of much investigation. We develop comparable results for the length as(w) of
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We find the exponential generating function for permutations with all valleys even and all peaks odd, and use it to determine the asymptotics for its coefficients, answering a question posed by Liviu
The On-Line Encyclopedia of Integer Sequences
  • N. Sloane
  • Computer Science
    Electron. J. Comb.
  • 1994
The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences which serves as a dictionary, to tell the user what is known about a particular sequence and is widely used.
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Introduction. A well-known algorithm for coloring the vertices of a graph is the "greedy algorithm": given a totally ordered set of colors, each vertex of the graph (taken in some order) is colored
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The number of alternating inversions is defined in the paper, in alternating (down-up) permutations, and a new $q-analog of the Euler number $E_n$ is obtained and shown how it emerges in a $q$-analogy of an identity expressing $E-n$ as a weighted sum of Dyck paths.