The computational challenge of enumerating high-dimensional rook walks

Manuel Kauers; Doron Zeilberger

doi:10.48550/arXiv.1011.4671

The computational challenge of enumerating high-dimensional rook walks

Manuel Kauers
, Doron Zeilberger

Research Institute for Symbolic Computation

Research output: Working paper and reports › Preprint

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.

Original language	English
Place of Publication	http://arxiv.org
Publisher	arXiv
Number of pages	5
DOIs	https://doi.org/10.48550/arXiv.1011.4671
Publication status	Published - Nov 2010

Publication series

Name	arXiv.org
No.	1011.4671

Fields of science

101001 Algebra
101002 Analysis
101 Mathematics
102 Computer Sciences
102011 Formal languages
101013 Mathematical logic
101020 Technical mathematics
101025 Number theory
101012 Combinatorics
101005 Computer algebra
101003 Applied geometry
102025 Distributed systems

JKU Focus areas

Computation in Informatics and Mathematics

Access to Document

10.48550/arXiv.1011.4671

Cite this

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