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arXiv · 1011.4671

The computational challenge of enumerating high-dimensional rook walks

Manuel Kauers·Doron Zeilberger
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Abstract

We provide guessed recurrence equations for the counting sequences of rook paths on d-dimensional chess boards starting at (0..0) and ending at (n..n), where d=2,3,...,12. Our recurrences suggest refined asymptotic formulas of these sequences. Rigorous proofs of the guessed recurrences as well as the suggested asymptotic forms are posed as challenges to the reader.

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Manuel Kauers, Doron Zeilberger. 2010-11-21. The computational challenge of enumerating high-dimensional rook walks. https://arxiv.org/abs/1011.4671

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