3 papers
math.CO2026
On the small-step quarter plane lattice walks with a non D-finite univariate generating function
Marni Mishna, Juan Pulido
We report on the status of the conjecture of Bousquet-Mélou and Mishna that the univariate counting generating function of a small-step quarter-plane lattice model is D-finite if…
math.CO2025
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…
math.CO2025
Differential transcendence and walks on self-similar graphs
Yakob Kahane, Marni Mishna
Symmetrically self-similar graphs are an important type of fractal graph. Their Green functions satisfy order one iterative functional equations. We show when the branching number…