Dimension of Posets

The dimension of a poset P is the least number t such that ther is an order preserving embedding from P to Rt. There is also an alternative definition via linear extensions of P.

Dimension theory is a mature discipline with interesting connections to various other branches of mathematics. To mention one: Dilworth proved that the dimension of a distributive lattice equals the width of the generating poset of the lattice (The famous duality theorem known as Dilworth's Theorem originally was formulated as a lemma in this context). To our work the following directions are most relevant: