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A combinatorial interpretation is provided for the moments of characteristic polynomials of random unitary matrices. This leads to a rather unexpected consequence of the Keating and Snaith conjecture: the moments of $|\zeta(1/2+it)|$ turn out to be connected with some increasing subsequence problems (such as the last passage percolation problem).doi:10.37236/1717 fatcat:ykuvbwdmpbe2xd33loggyzr7ti