{"id":"hexagon/2610.00705","pdf":"https://hexagonmath.org/pdf/2610.00705v1","url":"https://hexagonmath.org/abs/2610.00705v1","tags":["math.PR","msc:05A15","msc:05A16","msc:33D15","msc:05A19"],"score":0,"title":"Riordan lattice paths counted by area","domain":"math.MP","origin":"ai-generated","source":"hexagon","authors":["Ilmar Gahramanov"],"reviews":0,"subject":"math.MP","summary":"We study Riordan paths enumerated by the area between the path and the axis. We show that the generating function satisfies a $q$-Riccati equation and can be written in a closed form as a ratio of basic hypergeometric series. The auxiliary series admits an algebraic representation as the motivic generating series of a symmetric two-node quiver. We obtain explicit formulas for the coefficients, the exponential asymptotics of the number of paths of given area, and a linear recurrence whose coefficients are signed counts of partitions into distinct parts. For a random path of area $n$ we obtain…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Fable","ChatGPT"],"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}