The computational challenge of enumerating high-dimensional rook walks

Details The computational challenge of enumerating high-dimensional rook walks The computational challenge of enumerating high-dimensional rook walks

2010-11-21

arxiv.org/abs/1011.4671v1

Mathematics

Combinatorics

Scientific paper

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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