A new method for computing asymptotics of diagonal coefficients of multivariate generating functions

Alexander Raichev (1) , Mark C. Wilson (1)

1 Department of Computer Science [Auckland]

Let $\sum_{\mathbf{n} \in \mathbb{N}^d} F_{\mathbf{n}} \mathbf{x}^{\mathbf{n}}$ be a multivariate generating function that converges in a neighborhood of the origin of $\mathbb{C}^d$. We present a new, multivariate method for computing the asymptotics of the diagonal coefficients $F_{a_1n,\ldots,a_dn}$ and show its superiority over the standard, univariate diagonal method. Several examples are given in detail.

Mots clés: generating function; multivariate; asymptotics; diagonal

Domaines: Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]; Combinatoire [math.CO]; Géométrie algorithmique [cs.CG]

Alexander Raichev, Mark C. Wilson. A new method for computing asymptotics of diagonal coefficients of multivariate generating functions. 2007 Conference on Analysis of Algorithms, AofA 07, 2007, Juan les Pins, France. pp.485-496, ⟨10.46298/dmtcs.3531⟩. ⟨hal-01184779⟩