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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.

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
Software:
gfun; HYP; HYPERG; Mgfun; OEIS
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