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) `symbolicdynamicalprogramming' algorithms for computing many terms of `hard to compute sequences', namely the number of Latin trapezoids, generalized derangements, and generalized threerowed 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 Precursive in n. Our algorithms are fully implemented in Maple, and generated quite a few terms of such sequences.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.11285
 Bibcode:
 2021arXiv210811285S
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 12 pages. Accompanied by three Maple packages, and numerous output files, available from https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/ltrap.html