3 citations · 12 across the 17 of their papers we have counts for
18 papers · 1 filter
Restricted Jacobi permutations
Alyssa G. Henke, Kyle R. Hoffman, Derek H. Stephens +2
Jacobi permutations, introduced by Viennot in the context of Jacobi elliptic functions, are counted by the Euler numbers appearing in the series expansion $\sec x+\tan x=\s…
Zig-zag Eulerian polynomials
T. Kyle Petersen, Yan Zhuang
For any finite partially ordered set , the -Eulerian polynomial is the generating function for the descent number over the set of linear extensions of , and is closely rel…
On the statistic and valley-hopping
Nadia Lafrenière, Yan Zhuang
This paper studies the relationship between the modified Foata$\unicode{x2013}$Strehl action (a.k.a. valley-hopping)$\unicode{x2014}$a group action on permutations used to demonstr…
On kernels of descent statistics
William L. Clark, Yan Zhuang
The kernel of a descent statistic , introduced by Grinberg, is a subspace of the algebra of quasisymmetri…
Two-sided permutation statistics via symmetric functions
Ira M. Gessel, Yan Zhuang
Given a permutation statistic , define its inverse statistic by . We give a general approa…
Cyclic shuffle-compatibility via cyclic shuffle algebras
Jinting Liang, Bruce E. Sagan, Yan Zhuang
A permutation statistic is said to be shuffle-compatible if the distribution of over the set of shuffles of two disjoint permutations an…
A combinatorial proof of a symmetry for a refinement of the Narayana numbers
Miklós Bóna, Stoyan Dimitrov, Gilbert Labelle +4
We establish a tantalizing symmetry of certain numbers refining the Narayana numbers. In terms of Dyck paths, this symmetry is interpreted in the following way: if is t…
Statistics on clusters and -Stirling permutations
Sergi Elizalde, Justin M. Troyka, Yan Zhuang
The Goulden$\unicode{x2013}$Jackson cluster method, adapted to permutations by Elizalde and Noy, reduces the problem of counting permutations by occurrences of a prescribed consecu…
Fibonacci numbers, consecutive patterns, and inverse peaks
Justin M. Troyka, Yan Zhuang
We give multiple proofs of two formulas concerning the enumeration of permutations avoiding a monotone consecutive pattern with a certain value for the inverse peak number or inver…
A lifting of the Goulden-Jackson cluster method to the Malvenuto-Reutenauer algebra
Yan Zhuang
The Goulden-Jackson cluster method is a powerful tool for counting words by occurrences of prescribed subwords, and was adapted by Elizalde and Noy for counting permutations by occ…
Plethystic formulas for permutation enumeration
Ira M. Gessel, Yan Zhuang
We prove several general formulas for the distributions of various permutation statistics over any set of permutations whose quasisymmetric generating function is a symmetric funct…
Hopping from Chebyshev polynomials to permutation statistics
Jordan O. Tirrell, Yan Zhuang
We prove various formulas which express exponential generating functions counting permutations by the peak number, valley number, double ascent number, and double descent number st…
Shuffle-compatible permutation statistics
Ira M. Gessel, Yan Zhuang
Since the early work of Richard Stanley, it has been observed that several permutation statistics have a remarkable property with respect to shuffles of permutations. We formalize…
Eulerian polynomials and descent statistics
Yan Zhuang
We prove several identities expressing polynomials counting permutations by various descent statistics in terms of Eulerian polynomials, extending results of Stembridge, Petersen,…
A generalized Goulden-Jackson cluster method and lattice path enumeration
Yan Zhuang
The Goulden-Jackson cluster method is a powerful tool for obtaining generating functions for counting words in a free monoid by occurrences of a set of subwords. We introduce a gen…
Counting permutations by runs
Yan Zhuang
In his Ph.D. thesis, Ira Gessel proved a reciprocity formula for noncommutative symmetric functions which enables one to count words and permutations with restrictions on the lengt…
Counting permutations by alternating descents
Ira M. Gessel, Yan Zhuang
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 ques…
Shattering Thresholds for Random Systems of Sets, Words, and Permutations
Anant P. Godbole, Samantha Pinella, Yan Zhuang
This paper considers a problem that relates to the theories of covering arrays, permutation patterns, Vapnik-Chervonenkis (VC) classes, and probability thresholds. Specifically, we…