Dodgson condensation: The historical and mathematical development of an experimental method
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.
scientific article; zbMATH DE number 5289125
scientific article