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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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An upper bound on diagonal k-colored Ramsey number

I need a reference on any upper bound on $R(n, n, \dots, n)$ with $k$ arguments. For example, the standard recurrent bound gives something like $k^{kn}$, but I cannot find any written explicit bound.
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