Wilf classes of pairs of permutations of length 4

Ian Tuan-Yen Le

doi:10.37236/1922

Wilf classes of pairs of permutations of length 4

Ian Tuan-Yen Le^*

^*Corresponding author for this work

Mathematics

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

16 Scopus citations

Abstract

S_n(π₁ π₂, . . . , π_r) denotes the set of permutations of length n that have no subsequence with the same order relations as any of the π_i. In this paper we show that S_n(1342, 2143)| = |S_n(3142, 2341)| and S_n(1342, 3124)| = |S_n(1243, 2134)|. These two facts complete the classification of Wilf-equivalence classes for pairs of permutations of length four. In both instances we exhibit bijections between the sets using the idea of a "block", and in the former we find a generating function for |S_n(1342, 2143)|.

Original language	English (US)
Journal	Electronic Journal of Combinatorics
Volume	12
Issue number	1 R
DOIs	https://doi.org/10.37236/1922
State	Published - May 26 2005

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

Access to Document

10.37236/1922

Cite this

@article{82616ce3ab8b4d9ab6b34ba43dc4ea71,

title = "Wilf classes of pairs of permutations of length 4",

abstract = "Sn(π1 π2, . . . , πr) denotes the set of permutations of length n that have no subsequence with the same order relations as any of the πi. In this paper we show that Sn(1342, 2143)| = |Sn(3142, 2341)| and Sn(1342, 3124)| = |Sn(1243, 2134)|. These two facts complete the classification of Wilf-equivalence classes for pairs of permutations of length four. In both instances we exhibit bijections between the sets using the idea of a {"}block{"}, and in the former we find a generating function for |Sn(1342, 2143)|.",

author = "Le, {Ian Tuan-Yen}",

year = "2005",

month = may,

day = "26",

doi = "10.37236/1922",

language = "English (US)",

volume = "12",

journal = "Electronic Journal of Combinatorics",

issn = "1077-8926",

publisher = "Electronic Journal of Combinatorics",

number = "1 R",

}

TY - JOUR

T1 - Wilf classes of pairs of permutations of length 4

AU - Le, Ian Tuan-Yen

PY - 2005/5/26

Y1 - 2005/5/26

N2 - Sn(π1 π2, . . . , πr) denotes the set of permutations of length n that have no subsequence with the same order relations as any of the πi. In this paper we show that Sn(1342, 2143)| = |Sn(3142, 2341)| and Sn(1342, 3124)| = |Sn(1243, 2134)|. These two facts complete the classification of Wilf-equivalence classes for pairs of permutations of length four. In both instances we exhibit bijections between the sets using the idea of a "block", and in the former we find a generating function for |Sn(1342, 2143)|.

AB - Sn(π1 π2, . . . , πr) denotes the set of permutations of length n that have no subsequence with the same order relations as any of the πi. In this paper we show that Sn(1342, 2143)| = |Sn(3142, 2341)| and Sn(1342, 3124)| = |Sn(1243, 2134)|. These two facts complete the classification of Wilf-equivalence classes for pairs of permutations of length four. In both instances we exhibit bijections between the sets using the idea of a "block", and in the former we find a generating function for |Sn(1342, 2143)|.

UR - http://www.scopus.com/inward/record.url?scp=21244464234&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21244464234&partnerID=8YFLogxK

U2 - 10.37236/1922

DO - 10.37236/1922

M3 - Article

AN - SCOPUS:21244464234

SN - 1077-8926

VL - 12

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 1 R

ER -

Wilf classes of pairs of permutations of length 4

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this