## Moments of characteristic polynomials enumerate two-rowed lexicographic arrays.(English)Zbl 1033.15017

Electron. J. Comb. 10, Research paper R24, 8 p. (2003); printed version J. Comb. 10, No. 3 (2003).
The author gives an interpretation of moments of characteristic polynomials of random unitary matrices in terms of counts of two-rowed lexicographic arrays whose weakly increasing subsequences have at most $$N$$ elements. This connects the theory of these moments to last passage percolation theory, and gives a new interpretation of the conjecture J. P. Keating and N. C. Snaith [Commun. Math. Phys. 214, 57–89 (2000; Zbl 1051.11048)].

### MSC:

 15B52 Random matrices (algebraic aspects) 20G05 Representation theory for linear algebraic groups 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B43 Percolation 11M06 $$\zeta (s)$$ and $$L(s, \chi)$$

Zbl 1051.11048
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