A half-space approach to order dimension

Details A half-space approach to order dimension A half-space approach to order dimension

2007-02-17

arxiv.org/abs/math/0702509v1

Order 24 (2007) 59-73

Mathematics

Combinatorics

13 pages

Scientific paper

The aim of the present paper is to investigate the half-spaces in the
convexity structure of all quasiorders on a given set and to use them in an
alternative approach to classical order dimension. The main result states that
linear orders can almost always be replaced by half-space quasiorders in the
definition of the dimension of a partially ordered set.

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