Dodgson condensation: The historical and mathematical development of an experimental method
type: Item
instance of: scholarly article
title: Dodgson condensation: The historical and mathematical development of an experimental method
zbMATH Open document ID: 1151.15012
author: Francine F. Abeles
published in: Linear Algebra and its Applications
publication date: 2008-06-17T00:00:00Z
review text: In this expository paper the author describes the 19th century roots of the condensation method of Charles L. Dodgson (Lewis Carroll, 1832--1898) for the evaluation of determinants by computing only \(2\times 2\) minors, and the major steps on the path that began late in the 20th century with its emergence out of relative obscurity and led to its becoming a powerful tool in the automation of determinant evaluation. Dodgson used earlier results by Desanot (1819) and Jacobi (1833) in the proof of his method (1866). The first major modern step was made by \textit{D. P. Robbins} and \textit{H. Rumsey jun.} [Adv. Math. 62, 169--184 (1986; Zbl 0611.15008)] in their study of a certain key identity involving minors which is related to Dodgson's method and which led them to the discovery of the so-called alternating sign matrix (ASM) conjecture which was proved by \textit{D. Zeilberger} [Electron J. Comb. 3, No.~2, 283--366 (1996; Zbl 0858.05023)]. Dodgson condensation and ASMs have connections with combinatorics which are discussed by the author. In the last section of the paper the author discusses the role of Dodgson condensation in automated determinant evaluation.
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 65F40
Mathematics Subject Classification ID: 15-03
Mathematics Subject Classification ID: 01A55
zbMATH DE Number: 5289125
zbMATH Keywords: automation of determinant evaluations
zbMATH Keywords: determinantal identity
describes a project that uses: ROBBINS
describes a project that uses: rabbit
describes a project that uses: DODGSON
describes a project that uses: CLD
reviewed by: Rabe von Randow
MaRDI profile type: Publication
full work available at URL: j.laa.2007.11.022
OpenAlex ID: W2119072491
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DOI: 10.1016/J.LAA.2007.11.022
description: scientific article; zbMATH DE number 5289125