Alexander Raichev ; Mark C. Wilson
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A new method for computing asymptotics of diagonal coefficients of multivariate generating functions
dmtcs:3531 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2007,
DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07)
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https://doi.org/10.46298/dmtcs.3531
A new method for computing asymptotics of diagonal coefficients of multivariate generating functions
Authors: Alexander Raichev 1; Mark C. Wilson 1
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Alexander Raichev;Mark C. Wilson
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.
Wilson, Mark C, 2014, Diagonal Asymptotics For Products Of Combinatorial Classes, Combinatorics, Probability And Computing, 24, 1, pp. 354-372, 10.1017/s0963548314000625.