• Corpus ID: 235368239

Quasi-Stirling Permutations on Multisets

  title={Quasi-Stirling Permutations on Multisets},
  author={Sherry H.F.Yan and Lihong Yang and Yunwei Huang and Xue Zhu},
A permutation π of a multiset is said to be a quasi-Stirling permutation if there does not exist four indices i < j < k < ` such that πi = πk and πj = π`. Define QM(t, u, v) = ∑ π∈QM tuv, where QM denotes the set of quasi-Stirling permutations on the multiset M, and asc(π) (resp. des(π), plat(π)) denotes the number of ascents (resp. descents, plateaux) of π. Denote byMσ the multiset {1σ1 ,2σ2 , . . . , nσn}, where σ = (σ1, σ2, . . . , σn) is an n-composition of K for positive integers K and n… 

Figures from this paper



Descents on quasi-Stirling permutations

MacMahon's equidistribution theorem for k-Stirling permutations

Pattern restricted quasi-Stirling permutations

A bijection is constructed between quasi-Stirling permutations and the set of ordered rooted labeled trees and investigate pattern avoidance for these permutations.

The r-Multipermutations

Real Zeros and Normal Distribution for Statistics on Stirling Permutations Defined by Gessel and Stanley

  • M. Bóna
  • Mathematics
    SIAM J. Discret. Math.
  • 2009
It is proved that the generating function according to the number of descents has real roots only and is used to prove that the distribution of these descents and other equidistributed statistics on these objects converge to a normal distribution.

Inverse descents of r-multipermutations

Unimodal, log-concave and Pólya frequency sequences in combinatorics

Un grand nombre de suites d'interet combinatoire sont unimodales ou log-concaves. Il s'agit de proprietes difficiles a montrer et non conservees par des transformations lineaires, en general. On peut

Hilbert Polynomials in Combinatorics

We prove that several polynomials naturally arising in combinatorics are Hilbert polynomials of standard graded commutative k-algebras.

Stirling Polynomials

Yeliussizov, Stirling permutations on multisets

  • European J. Combin.,
  • 2014