2021/08/25 by George Spahn, Doron Zeilberger, Spahn, George +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2108.11285
openalex publication_date 2021/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this case study in ``fully automated enumeration'', we illustrate how to take full advantage of symbolic computation by developing (what we call) `symbolic-dynamical-programming' algorithms for computing many terms of `hard to compute sequences', namely the number of Latin trapezoids, generalized derangements, and generalized three-rowed Latin rectangles. At the end we also sketch the proof of a generalization of Ira Gessel's 1987 theorem that says that for any number of rows, k, the number of Latin rectangles with k rows and n columns is P-recursive in n. Our algorithms are fully implemented in Maple, and generated quite a few terms of such sequences.