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

Abstract : 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.
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Communication dans un congrès
Jacquet, Philippe. 2007 Conference on Analysis of Algorithms, AofA 07, 2007, Juan les Pins, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07), pp.485-496, 2007, DMTCS Proceedings
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Alexander Raichev, Mark C. Wilson. A new method for computing asymptotics of diagonal coefficients of multivariate generating functions. Jacquet, Philippe. 2007 Conference on Analysis of Algorithms, AofA 07, 2007, Juan les Pins, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07), pp.485-496, 2007, DMTCS Proceedings. 〈hal-01184779〉

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