3 papers
math.CO2025
Distribution of the roots of Eulerian polynomials
Paul Melotti
We give a new proof that the empirical measures of the roots of Eulerian polynomials converge to a certain log-Cauchy distribution. To do so, we show that each moment of the roots…
math.DS2024
The Schwarzian octahedron recurrence (dSKP equation) II: geometric systems
Niklas Christoph Affolter, Béatrice de Tilière, Paul Melotti
We consider nine geometric systems: Miquel dynamics, P-nets, integrable cross-ratio maps, discrete holomorphic functions, orthogonal circle patterns, polygon recutting, circle inte…
math.CO2024
The Schwarzian octahedron recurrence (dSKP equation) I: explicit solutions
Niklas Christoph Affolter, Béatrice de Tilière, Paul Melotti
We prove an explicit expression for the solutions of the discrete Schwarzian octahedron recurrence, also known as the discrete Schwarzian KP equation (dSKP), as the ratio of two pa…