Differential equations satisfied by generating functions of 5-, 6-, and 7-regular labelled graphs: a reduction-based approach

2024/06/07 by Chyzak, Frédéric, Mishna, Marni · 1 citation
#05C30 #12H05 #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Symbolic Computation (cs.SC)

paper · doi:10.48550/arxiv.2406.04753

Abstract

By a classic result of Gessel, the exponential generating functions for k-regular graphs are D-finite. Using Gröbner bases in Weyl algebras, we compute the linear differential equations satisfied by the generating function for 5-, 6-, and 7- regular graphs. The method is sufficiently robust to consider variants such as graphs with multiple edges, loops, and graphs whose degrees are limited to fixed sets of values.

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• Faster multivariate integration in D-modules

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