Moments of characteristic polynomials enumerate two-rowed lexicographic arrays
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 $\midξ(1/2+it)\mid$ turn out to be connected with some increasing subsequences problems (such as the last passage percolation problem).
math-ph↗