A refined sign-balance of simsun permutations

Sen-Peng Eu, Tung Shan Fu, Yeh Jong Pan

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We present a refined sign-balance result for simsun permutations. On the basis of our previously established bijection between simsun permutations and increasing 1-2 trees, we deduce the recurrence relation and exponential generating function for the sign-balance of simsun permutations of length n with k descents. For odd lengths, the distribution turns out to be (shifted) second-order Eulerian numbers. For even lengths, the distribution forms a signed triangle whose row sums are all zeros. Meanwhile, we obtain two Pólya frequency sequences, one of which refines the double factorial of the odd numbers and the other, that of the even numbers.

Original languageEnglish
Pages (from-to)97-109
Number of pages13
JournalEuropean Journal of Combinatorics
Volume36
DOIs
Publication statusPublished - 2014 Feb 1

Fingerprint

Permutation
Eulerian numbers
Exponential Generating Function
Even number
Odd number
Factorial
Recurrence relation
Signed
Descent
Bijection
Deduce
Triangle
Odd
Zero
Form

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

A refined sign-balance of simsun permutations. / Eu, Sen-Peng; Fu, Tung Shan; Pan, Yeh Jong.

In: European Journal of Combinatorics, Vol. 36, 01.02.2014, p. 97-109.

Research output: Contribution to journalArticle

Eu, Sen-Peng ; Fu, Tung Shan ; Pan, Yeh Jong. / A refined sign-balance of simsun permutations. In: European Journal of Combinatorics. 2014 ; Vol. 36. pp. 97-109.
@article{5ca4c284b45d4403bdf387400a728a15,
title = "A refined sign-balance of simsun permutations",
abstract = "We present a refined sign-balance result for simsun permutations. On the basis of our previously established bijection between simsun permutations and increasing 1-2 trees, we deduce the recurrence relation and exponential generating function for the sign-balance of simsun permutations of length n with k descents. For odd lengths, the distribution turns out to be (shifted) second-order Eulerian numbers. For even lengths, the distribution forms a signed triangle whose row sums are all zeros. Meanwhile, we obtain two P{\'o}lya frequency sequences, one of which refines the double factorial of the odd numbers and the other, that of the even numbers.",
author = "Sen-Peng Eu and Fu, {Tung Shan} and Pan, {Yeh Jong}",
year = "2014",
month = "2",
day = "1",
doi = "10.1016/j.ejc.2013.05.001",
language = "English",
volume = "36",
pages = "97--109",
journal = "European Journal of Combinatorics",
issn = "0195-6698",
publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - A refined sign-balance of simsun permutations

AU - Eu, Sen-Peng

AU - Fu, Tung Shan

AU - Pan, Yeh Jong

PY - 2014/2/1

Y1 - 2014/2/1

N2 - We present a refined sign-balance result for simsun permutations. On the basis of our previously established bijection between simsun permutations and increasing 1-2 trees, we deduce the recurrence relation and exponential generating function for the sign-balance of simsun permutations of length n with k descents. For odd lengths, the distribution turns out to be (shifted) second-order Eulerian numbers. For even lengths, the distribution forms a signed triangle whose row sums are all zeros. Meanwhile, we obtain two Pólya frequency sequences, one of which refines the double factorial of the odd numbers and the other, that of the even numbers.

AB - We present a refined sign-balance result for simsun permutations. On the basis of our previously established bijection between simsun permutations and increasing 1-2 trees, we deduce the recurrence relation and exponential generating function for the sign-balance of simsun permutations of length n with k descents. For odd lengths, the distribution turns out to be (shifted) second-order Eulerian numbers. For even lengths, the distribution forms a signed triangle whose row sums are all zeros. Meanwhile, we obtain two Pólya frequency sequences, one of which refines the double factorial of the odd numbers and the other, that of the even numbers.

UR - http://www.scopus.com/inward/record.url?scp=84882937091&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84882937091&partnerID=8YFLogxK

U2 - 10.1016/j.ejc.2013.05.001

DO - 10.1016/j.ejc.2013.05.001

M3 - Article

AN - SCOPUS:84882937091

VL - 36

SP - 97

EP - 109

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

SN - 0195-6698

ER -