Asymptotics of Clebsch–Gordan coefficients

On the asymptotics of Kronecker coefficients, 2

Kronecker coefficients encode the tensor products of complex irreducible representations of symmetric groups. Their stability properties have been considered recently by several authors (Vallejo, Pak and Panova, Stembridge). In [3] we described a geometric method, based on Schur-Weyl duality, that allows to produce huge series of instances of this phenomenon. In this note we show how to go beyo...

On the asymptotics of Kronecker coefficients

Coefficients of algebraic functions: formulae and asymptotics

This paper studies the coefficients of algebraic functions. First, we recall the too-little-known fact that these coefficients fn have a closed form. Then, we study their asymptotics, known to be of the type fn ∼ CAn. When the function is a power series associated to a context-free grammar, we solve a folklore conjecture: the appearing critical exponents α can not be 1/3 or −5/2, they in fact b...

Asymptotics of diagonal coefficients of multivariate generating functions

Let ∑ n∈Nd fnx n be a multivariate generating function that converges in a neighborhood of the origin of Cd. We present a general theorem for computing the asymptotics of the diagonal coefficients fa1n,...,adn.

Automatic asymptotics for coefficients of smooth, bivariate rational functions

We consider a bivariate rational generating function F (x, y) = P (x, y) Q(x, y) = ∑ r,s≥0 arsx y under the assumption that the complex algebraic curve V on which Q vanishes is smooth. Formulae for the asymptotics of the coefficients {ars} are derived in [PW02]. These formulae are in terms of algebraic and topological invariants of V, but up to now these invariants could be computed only under ...