Recursion relations for Unitary integrals, Combinatorics and the Toeplitz Lattice

Mark Adler Pierre van Moerbeke

The Toeplitz determinants (of increasing size) associated with the symbols $expt(z+z^{-1})$ or $(1-\xi z{)}^{\alpha }(1-\xi z^{-1}{)}^{\beta }$ satisfy recursion relations, thus expressing all the T…