Wilf classes of pairs of permutations of length 4

Ian Le

doi:10.37236/1922

Wilf classes of pairs of permutations of length 4

Ian Le^*

^*Corresponding author for this work

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

16 Citations (Scopus)

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
Journal	Electronic Journal of Combinatorics
Volume	12
Issue number	1 R
DOIs	https://doi.org/10.37236/1922
Publication status	Published - 26 May 2005
Externally published	Yes

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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)|.",

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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)|.

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Wilf classes of pairs of permutations of length 4

Abstract

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