ISSN:
1572-9273
Keywords:
Primary 06A10
;
secondary 06A05
;
poset
;
N-free
;
(greedy) linear extension
;
(greedy) dimension
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This paper introduces a new concept of dimension for partially ordered sets. Dushnik and Miller in 1941 introduced the concept of dimension of a partial order P, as the minimum cardinality of a realizer, (i.e., a set of linear extensions of P whose intersection is P). Every poset has a greedy realizer (i.e., a realizer consisting of greedy linear extensions). We begin the study of the notion of greedy dimension of a poset and its relationship with the usual dimension by proving that equality holds for a wide class of posets including N-free posets, two-dimensional posets and distributive lattices.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00383597
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