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math.CO2026
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…
math.CO2025
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…
math.CO2024
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 eq…