2023/05/15 by AJ Bu, Doron Zeilberger, Bu, AJ +1
Computer Science · #Advanced Database Systems and Queries #Combinatorics (math.CO) #Data Management and Algorithms #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2305.09030
openalex publication_date 2023/05/15 · openalex created_date 2023/05/18 · openalex updated_date 2026/07/28
We show the power of Bruno Buchberger's seminal Groebner Basis algorithm, interfaced, seamlessly, with what we call symbolic dynamical programming, to automatically generate algebraic equations satisfied by the generating functions enumerating so-called Generalized Dyck Walks, i.e. 2D walks that start and end on the x-axis, and never dip below it, for an arbitrary set of steps. More impressively, we combine it with calculus (that Maple knows very well!), to automatically compute generating functions for the sum-of-the-areas of these generalized Dyck paths, and even for the sum of any given power of the areas, enabling us to get statistical information about the area under a random generalized Dyck path.