The sorting index on colored permutations and even-signed permutations

Sen-Peng Eu, Yuan Hsun Lo, Tsai Lien Wong

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We define a new statistic sor on the set of colored permutations Gr,n and prove that it has the same distribution as the length function. For the set of restricted colored permutations corresponding to the arrangements of n non-attacking rooks on a fixed Ferrers shape we show that the following two sequences of set-valued statistics are joint equidistributed: (ℓ,Rmil0,Rmil1,...,Rmilr-1, Lmil0,Lmil1,...,Lmilr-1, Lmal0,Lmal1,...,Lmalr-1, Lmap0,Lmap1,...,Lmapr-1) and (sor,Cyc0,Cycr-1,...,Cyc1, Lmic0,Lmicr-1,...,Lmic1, Lmal0,Lmal1,...,Lmalr-1, Lmap0,Lmap1,...,Lmapr-1). Analogous results are also obtained for Coxeter group of type D. Our work generalizes recent results of Petersen, Chen-Gong-Guo and Poznanović.

Original languageEnglish
Pages (from-to)18-50
Number of pages33
JournalAdvances in Applied Mathematics
Volume68
DOIs
Publication statusPublished - 2015 Jul 1

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Even permutation
Signed Permutations
Sorting
Permutation
Statistics
Coxeter Group
Statistic
Arrangement
Generalise

Keywords

  • Coxeter group
  • Joint equidistribution
  • Set-valued statistics
  • Sorting index

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

The sorting index on colored permutations and even-signed permutations. / Eu, Sen-Peng; Lo, Yuan Hsun; Wong, Tsai Lien.

In: Advances in Applied Mathematics, Vol. 68, 01.07.2015, p. 18-50.

Research output: Contribution to journalArticle

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N2 - We define a new statistic sor on the set of colored permutations Gr,n and prove that it has the same distribution as the length function. For the set of restricted colored permutations corresponding to the arrangements of n non-attacking rooks on a fixed Ferrers shape we show that the following two sequences of set-valued statistics are joint equidistributed: (ℓ,Rmil0,Rmil1,...,Rmilr-1, Lmil0,Lmil1,...,Lmilr-1, Lmal0,Lmal1,...,Lmalr-1, Lmap0,Lmap1,...,Lmapr-1) and (sor,Cyc0,Cycr-1,...,Cyc1, Lmic0,Lmicr-1,...,Lmic1, Lmal0,Lmal1,...,Lmalr-1, Lmap0,Lmap1,...,Lmapr-1). Analogous results are also obtained for Coxeter group of type D. Our work generalizes recent results of Petersen, Chen-Gong-Guo and Poznanović.

AB - We define a new statistic sor on the set of colored permutations Gr,n and prove that it has the same distribution as the length function. For the set of restricted colored permutations corresponding to the arrangements of n non-attacking rooks on a fixed Ferrers shape we show that the following two sequences of set-valued statistics are joint equidistributed: (ℓ,Rmil0,Rmil1,...,Rmilr-1, Lmil0,Lmil1,...,Lmilr-1, Lmal0,Lmal1,...,Lmalr-1, Lmap0,Lmap1,...,Lmapr-1) and (sor,Cyc0,Cycr-1,...,Cyc1, Lmic0,Lmicr-1,...,Lmic1, Lmal0,Lmal1,...,Lmalr-1, Lmap0,Lmap1,...,Lmapr-1). Analogous results are also obtained for Coxeter group of type D. Our work generalizes recent results of Petersen, Chen-Gong-Guo and Poznanović.

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