Automatic Counting of Generalized Latin Rectangles and Trapezoids
Abstract
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.
Keywords
Cite
@article{arxiv.2108.11285,
title = {Automatic Counting of Generalized Latin Rectangles and Trapezoids},
author = {George Spahn and Doron Zeilberger},
journal= {arXiv preprint arXiv:2108.11285},
year = {2021}
}
Comments
12 pages. Accompanied by three Maple packages, and numerous output files, available from https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/ltrap.html