Permutation statistics and linear extensions of posets

Anders Björner, Michelle L Galloway

Research output: Contribution to journalArticle

53 Citations (Scopus)

Abstract

We consider subsets of the symmetric group for which the inversion index and major index are equally distributed. Our results extend and unify results of MacMahon, Foata, and Schützenberger, and the authors. The sets of permutations under study here arise as linear extensions of labeled posets, and more generally as order closed subsets of a partial ordering of the symmetric group called the weak order. For naturally labeled posets, we completely characterize. as postorder labeled forests, those posets whose linear extension set is equidistributed. A bijection of Foata which takes major index to inversion index plays a fundamental role in our study of equidistributed classes of permutations. We also explore, here, classes of permutations which are invariant under Foata's bijection.

Original languageEnglish (US)
Pages (from-to)85-114
Number of pages30
JournalJournal of Combinatorial Theory, Series A
Volume58
Issue number1
DOIs
StatePublished - 1991

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Permutation Statistics
Linear Extension
Set theory
Poset
Major Index
Permutation
Statistics
Bijection
Symmetric group
Inversion
Weak Order
Subset
Partial ordering
Closed
Invariant
Class

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Permutation statistics and linear extensions of posets. / Björner, Anders; Galloway, Michelle L.

In: Journal of Combinatorial Theory, Series A, Vol. 58, No. 1, 1991, p. 85-114.

Research output: Contribution to journalArticle

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