Title :
On the generation of d-ordered sets: a proof based on determinant theory
Author_Institution :
City Coll. of New York, NY, USA
fDate :
5/1/1992 12:00:00 AM
Abstract :
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
Keywords :
matrix algebra; set theory; Laplacian expansion; bordered determinant; columns; d-ordered sets; determinant theory; transpositions; Application software; Circuits; Cities and towns; Computer science; Cryptography; Geometry; Laplace equations; Mathematics; Multidimensional systems; Sorting;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
