Clifford algebra and 4-color theorem
type: Item
instance of: scholarly article
title: Clifford algebra and 4-color theorem
zbMATH Open document ID: 0856.15025
author: Collin C. Carbno
published in: Advances in Applied Clifford Algebras
publication date: 1997-02-24T00:00:00Z
review text: The 4-color theorem was shown to be equivalent to a statement of bracketing of cross products of orthogonal vectors in three space by Kaufmann. This paper establishes a constructive proof of the 4-color theorem by employing Clifford algebras. The associative Clifford product can be used to model the cross product which renders bracketing to be obsolete. The proof proceeds as follows: (1) If two bracketings of cross products of \(n\) orthogonal vectors are nonzero, then they are identical. (2) The nature and number of inequalities obtained from bracketing are studied, which results in \(2n-3\) inequalities to be satisfied. (3) The existence of a nonzero choice of such orthogonal vectors is shown, which completes the proof.
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 05B45
zbMATH DE Number: 915228
zbMATH Keywords: Clifford algebra
zbMATH Keywords: 4-color theorem
zbMATH Keywords: cross product
reviewed by: Bertfried Fauser
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 915228