Sign imbalances of snakes and valley-signed permutations

Huilan Chang; Sen Peng Eu; Yuan Hsun Lo

doi:10.1016/j.aam.2014.05.004

Sign imbalances of snakes and valley-signed permutations

Huilan Chang
, Sen Peng Eu
, Yuan Hsun Lo^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

One of the combinatorial structures counted by the Springer numbers is the set of snakes, which in type A_n is the set of the alternating permutations and in type B_n (or D_n) is the set of certain signed permutations. The set of valley-signed permutations, defined by Josuat-Vergès, Novelli and Thibon, is another structure counted by the Springer numbers of type B_n (or D_n). In this paper we determine the sign imbalances of these sets of snakes and valley-signed permutations under various inversion statistics inv_w, inv _o, inv_s, inv_B, and inv_D.

Original language	English
Pages (from-to)	26-47
Number of pages	22
Journal	Advances in Applied Mathematics
Volume	59
DOIs	https://doi.org/10.1016/j.aam.2014.05.004
Publication status	Published - 2014 Aug
Externally published	Yes

Keywords

Alternating permutation
Inversions
Sign imbalance
Snake
Valley-signed permutation

ASJC Scopus subject areas

Applied Mathematics

Access to Document

10.1016/j.aam.2014.05.004

Cite this

@article{7542ce2ba87b4dc1a1f8377a96d7b4dd,

title = "Sign imbalances of snakes and valley-signed permutations",

abstract = "One of the combinatorial structures counted by the Springer numbers is the set of snakes, which in type An is the set of the alternating permutations and in type Bn (or Dn) is the set of certain signed permutations. The set of valley-signed permutations, defined by Josuat-Verg{\`e}s, Novelli and Thibon, is another structure counted by the Springer numbers of type Bn (or Dn). In this paper we determine the sign imbalances of these sets of snakes and valley-signed permutations under various inversion statistics invw, inv o, invs, invB, and invD.",

keywords = "Alternating permutation, Inversions, Sign imbalance, Snake, Valley-signed permutation",

author = "Huilan Chang and Eu, \{Sen Peng\} and Lo, \{Yuan Hsun\}",

note = "Funding Information: Partially supported by National Science Council of Taiwan under grants NSC 101-2115-M-390-004-MY3 (S.-P. Eu and Y.-H. Lo) and NSC 100-2115-M-390-004-MY2 (H. Chang). ",

year = "2014",

month = aug,

doi = "10.1016/j.aam.2014.05.004",

language = "English",

volume = "59",

pages = "26--47",

journal = "Advances in Applied Mathematics",

issn = "0196-8858",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Sign imbalances of snakes and valley-signed permutations

AU - Chang, Huilan

AU - Eu, Sen Peng

AU - Lo, Yuan Hsun

N1 - Funding Information: Partially supported by National Science Council of Taiwan under grants NSC 101-2115-M-390-004-MY3 (S.-P. Eu and Y.-H. Lo) and NSC 100-2115-M-390-004-MY2 (H. Chang).

PY - 2014/8

Y1 - 2014/8

N2 - One of the combinatorial structures counted by the Springer numbers is the set of snakes, which in type An is the set of the alternating permutations and in type Bn (or Dn) is the set of certain signed permutations. The set of valley-signed permutations, defined by Josuat-Vergès, Novelli and Thibon, is another structure counted by the Springer numbers of type Bn (or Dn). In this paper we determine the sign imbalances of these sets of snakes and valley-signed permutations under various inversion statistics invw, inv o, invs, invB, and invD.

AB - One of the combinatorial structures counted by the Springer numbers is the set of snakes, which in type An is the set of the alternating permutations and in type Bn (or Dn) is the set of certain signed permutations. The set of valley-signed permutations, defined by Josuat-Vergès, Novelli and Thibon, is another structure counted by the Springer numbers of type Bn (or Dn). In this paper we determine the sign imbalances of these sets of snakes and valley-signed permutations under various inversion statistics invw, inv o, invs, invB, and invD.

KW - Alternating permutation

KW - Inversions

KW - Sign imbalance

KW - Snake

KW - Valley-signed permutation

UR - https://www.scopus.com/pages/publications/84905592525

UR - https://www.scopus.com/pages/publications/84905592525#tab=citedBy

U2 - 10.1016/j.aam.2014.05.004

DO - 10.1016/j.aam.2014.05.004

M3 - Article

AN - SCOPUS:84905592525

SN - 0196-8858

VL - 59

SP - 26

EP - 47

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

ER -

Sign imbalances of snakes and valley-signed permutations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this