Advanced Determinant Calculus: A Complement

Abstract

This is a complement to my previous article "Advanced Determinant Calculus" (Séminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described in the previous article in order to solve a particular problem from number theory (G. Almkvist, J. Petersson and the author, Experiment. Math. 12 (2003), 441-456). Moreover, I add a list of determinant evaluations which I consider as interesting, which have been found since the appearance of the previous article, or which I failed to mention there, including several conjectures and open problems.

AmS-LaTeX, 85 pages; Final, largely revised version

References in corpus (9)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Alternating sign matrices and domino tilings
• Another proof of the alternating sign matrix conjecture
• Summation and transformation formulas for elliptic hypergeometric series
• Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations
• Plane partitions I: a generalization of MacMahon's formula
• Enumeration of Symmetry Classes of Alternating Sign Matrices and Characters of Classical Groups
• On the computation of the n^th decimal digit of various transcendental numbers
• Rectangular Scott-type Permanents