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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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Where in mathematics do these polynomials appear?
I have just found this closed form for f and hope it might help a bit and verified it for $ k=1, 2, 3, 4 $here the formula $ f_k (x)= \binom{k}{k}(x^2)^{2^{k-1}}-\binom{k}{k-1} (x^2)^{2^{k-2}}+\binom …