Abstract :
This is a complement to my previous article “Advanced Determinant Calculus” [C. Krattenthaler, Advanced determinant calculus, Séminaire Lotharingien Combin. 42 (1999) (“The Andrews Festschrift”), 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, C. Krattenthaler, J. Petersson, Some new formulas for π, 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
Keywords :
Cauchy’s double alternant , Non-intersecting lattice paths , Non-crossing partitions , Skew circulant matrix , plane partitions , Perfect matchings , Confluent alternant , Tableaux , Permutations , Confluent Cauchy determinant , Rhombus tilings , signed permutations , Pfaffian , lozenge tilings , Inversion number , Hankel determinants , Alternating sign matrices , Integer partitions , Meixner polynomials , Compositions , Chebyshev polynomials , Non-commutative symmetric functions , continued fractions , Elliptic functions , Binomial coefficient , The number ? , Catalan numbers , LLL-algorithm , Fibonacci numbers , Major index , orthogonal polynomials , Determinants , Bernoulli numbers , Vandermonde determinant , Stirling numbers , Descent algebra , Laguerre polynomials
