| Determinants through the looking glass (2009) | |||||||||||||||
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| dedicated to dominique foata on his 65th birthday Using a recurrence derived from Dodgson’s Condensation Method, we provide numerous explicit evaluations of determinants. They were all conjectured, and then rigorously proved, by computer-assisted methods, that should be amenable to full automation. We also mention a first step towards that goal, our Maple package, DODGSON, that automates the special case of Hankel and Toeplitz hypergeometric determinants. © 2001 Elsevier Science Key Words: Hankel/Toeplitz hypergeometric determinants; Dodgson’s condensation method. This article is motivated by the computation in [1] that was inspired by the short proof [6] of MacMahon’s determinant evaluation [4], using a determinantal identity of Charles Dodgson [2]. Many special cases of the sampled determinants given belowwere independently discovered by Petkov˘sek [5]. For an excellent and detailed survey of existing methods of proofs of determinant identities, see [3]. For any n by n matrix A, let A r�i � j � denote the r by r minor consisting of r contiguous rows and columns of A, starting with row i and column j. | |||||||||||||||
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