A study of the order dimension of a poset using matrices

Abstract

In every finite poset (X, ≤ ) we assign the so called order-matrix A^≤_X = (α_ij), where α_ij ∈ {−2, 0, 1, 2}. Using this matrix, we characterize the order dimension of an arbitrary finite poset.

Keywords: Poset, linear extension, order dimension, matrix theory