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arXiv · 2108.11285

Automatic Counting of Generalized Latin Rectangles and Trapezoids

George Spahn·Doron Zeilberger
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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.

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George Spahn, Doron Zeilberger. 2021-08-25. Automatic Counting of Generalized Latin Rectangles and Trapezoids. https://arxiv.org/abs/2108.11285

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