Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9498136 | Linear Algebra and its Applications | 2005 | 99 Pages |
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 Ï, 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
11B73primary 05A19Inversion number33E0533D4505A1511B6805A1811Y6005E1005E1533C4505A3005A1715A1511C20CompositionsStirling numbersBernoulli numbersFibonacci numbersHankel determinantsVandermonde determinantSigned permutationsRhombus tilingsLozenge tilingsElliptic functionspermutationsDescent algebraTableauxPerfect matchingsMajor indexCatalan numbersBinomial coefficientDeterminantsAlternating sign matricesNon-intersecting lattice pathsNon-crossing partitionsInteger partitionsPlane partitionsPfaffianChebyshev polynomialsLaguerre polynomialsMeixner polynomialsOrthogonal polynomialsContinued fractions
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
C. Krattenthaler,