We revisit the work of the first named author and using simpler algebraic arguments we
calculate integrals of polynomial functions with respect to the Haar measure on the unitary …

We consider integrals on unitary groups U d of the form ?U_dU_i_1?j_1⋯U_i_q?j_qU_j^'_1i
^'_1^∗⋯U_j^'_q^'i^'_q^'^∗dU. We give an explicit formula in terms of characters of …

Tensor models generalize random matrix models in yielding a theory of dynamical
triangulations in arbitrary dimensions. Colored tensor models have been shown to admit a …

We compare the physics potential of planned superbeams with the one of neutrino factories.
Therefore, the experimental setups as well as the most relevant uncertainties and errors are …

We extend Schaeffer's bijection between rooted quadrangulations and well-labeled trees to
the general case of Eulerian planar maps with prescribed face valences, to obtain a bijection …

We derive the exact generating function for planar maps (genus zero fatgraphs) with vertices
of arbitrary even valence and with two marked points at a fixed geodesic distance. This is …

Multiparametric families of hypergeometric τ-functions of KP or Toda type serve as
generating functions for weighted Hurwitz numbers, providing weighted enumerations of …

Let F (t, u)≡ F (u) be a formal power series in t with polynomial coefficients in u. Let F1,…, Fk
be k formal power series in t, independent of u. Assume all these series are characterized by …

A considerable number of asymptotic distributions arising in random combinatorics and
analysis of algorithms are of the exponential‐quadratic type, that is, Gaussian. We exhibit a …

Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together
the work of today's most prominent researchers. The first two chapters provide a …