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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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