On the generation of d-ordered sets: a proof based on determinant theory

摘要

A simple proof of the theorem of determinants that yields d-ordered sets is given. Nothing more complicated than the Laplacian expansion of a determinant is used in the proof, which consists essentially of two parts. First a bordered determinant is used to yield the necessary determinantal equation. Then, transpositions of columns bring the minors in the equation into the required form so that they satisfy the conditions for a d-ordered set.