Signed posets

Victor Reiner

Research output: Contribution to journalReview articlepeer-review

28 Scopus citations

Abstract

We define a new object, called a signed poset, that bears the same relation to the hyperoctahedral group Bn (i.e., signed permutations on n letters), as do posets to the symmetric group Sn. We then prove hyperoctahedral analogues of the following results: (1) the generating function results from the theory of P-partitions; (2) the fundamental theorem of finite distributive lattices (or Birkhoff's theorem) relating a poset to its distributive lattice of order ideals; (3) the edgewise-lexicographic shelling of upper-semimodular lattices; (4) MacMahon's calculation of the distribution of the major index for permutations.

Original languageEnglish (US)
Pages (from-to)324-360
Number of pages37
JournalJournal of Combinatorial Theory, Series A
Volume62
Issue number2
DOIs
StatePublished - Mar 1993

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