TY - JOUR

T1 - Signed posets

AU - Reiner, Victor

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 1993/3

Y1 - 1993/3

N2 - 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.

AB - 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.

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U2 - 10.1016/0097-3165(93)90052-A

DO - 10.1016/0097-3165(93)90052-A

M3 - Review article

AN - SCOPUS:38249006671

VL - 62

SP - 324

EP - 360

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 2

ER -