The computational challenge of enumerating high-dimensional rook walks
Combinatorics
2010-11-23 v1
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.
Cite
@article{arxiv.1011.4671,
title = {The computational challenge of enumerating high-dimensional rook walks},
author = {Manuel Kauers and Doron Zeilberger},
journal= {arXiv preprint arXiv:1011.4671},
year = {2010}
}