4 papers
On (3,1)-regular graphs with one more vertex than edges
Frédéric Chyzak, Hui Huang, Manuel Kauers
Sequence A339987 of the OEIS counts (3,1)-regular graphs having one more vertex than edges by half the number of vertices. A recurrence relation satisfied by this sequence was gues…
Faster multivariate integration in D-modules
Hadrien Brochet, Frédéric Chyzak, Pierre Lairez
We present a new algorithm for solving the reduction problem in the context of holonomic integrals, which in turn provides an approach to integration with parameters. Our method ex…
Single-exponential bounds for diagonals of D-finite power series
Shaoshi Chen, Frédéric Chyzak, Pingchuan Ma +1
D-finite power series appear ubiquitously in combinatorics, number theory, and mathematical physics. They satisfy systems of linear partial differential equations whose solution sp…
Differential equations satisfied by generating functions of 5-, 6-, and 7-regular labelled graphs: a reduction-based approach
Frédéric Chyzak, Marni Mishna
By a classic result of Gessel, the exponential generating functions for -regular graphs are D-finite. Using Gröbner bases in Weyl algebras, we compute the linear differential e…