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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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Asymptotics and combinatorics
Wright's expansion of
$$
(1-z)^b\exp[A/(1-z)^c], \text{for } A > 0, 0<c<1\tag{1}
$$
is, in the words of the late, great Mark Kac "well known to those that know it well".
(See, for example, p563 of F …