Advanced determinant calculus. (English) Zbl 0923.05007
The paper surveys techniques and results on advanced determinant evaluation. A few useful and efficient techniques are shown, an extensive list of evaluated determinants are given, including the context in which they came up, and further references to determinant evaluations. The determinant evaluations surveyed here show connection to special sequences of numbers and polynomials, and to enumerative combinatorics.
Reviewer: L.A.Székely (Columbia/South Carolina)
MSC:
05A19 | Combinatorial identities, bijective combinatorics |
05A10 | Factorials, binomial coefficients, combinatorial functions |
05A15 | Exact enumeration problems, generating functions |
05A18 | Partitions of sets |
05A30 | \(q\)-calculus and related topics |
05E15 | Combinatorial aspects of groups and algebras (MSC2010) |
11B68 | Bernoulli and Euler numbers and polynomials |
11B73 | Bell and Stirling numbers |
11C20 | Matrices, determinants in number theory |
05A17 | Combinatorial aspects of partitions of integers |
05E10 | Combinatorial aspects of representation theory |
15A15 | Determinants, permanents, traces, other special matrix functions |
33C65 | Appell, Horn and Lauricella functions |
33D70 | Other basic hypergeometric functions and integrals in several variables |