The computational challenge of enumerating high-dimensional rook walks

Manuel Kauers; Doron Zeilberger

doi:10.1016/j.aam.2011.03.004

The computational challenge of enumerating high-dimensional rook walks

Manuel Kauers, Doron Zeilberger

SAS - Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We present guesses, based on intensive computer algebra calculations, for recurrence equations of the sequences enumerating rook walks in up to twelve dimensions ending on the main diagonal. Computer proofs can in principle be constructed for all of them. For the moment, however, these computations are feasible only for low dimensions. We pose it as a challenge to develop algorithms which can also certify the correctness of the equations we found for the higher dimensions.

Original language	English (US)
Pages (from-to)	813-819
Number of pages	7
Journal	Advances in Applied Mathematics
Volume	47
Issue number	4
DOIs	https://doi.org/10.1016/j.aam.2011.03.004
State	Published - Oct 2011

All Science Journal Classification (ASJC) codes

Applied Mathematics

Keywords

Automated guessing
Computer algebra
Lattice walks

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title = "The computational challenge of enumerating high-dimensional rook walks",

abstract = "We present guesses, based on intensive computer algebra calculations, for recurrence equations of the sequences enumerating rook walks in up to twelve dimensions ending on the main diagonal. Computer proofs can in principle be constructed for all of them. For the moment, however, these computations are feasible only for low dimensions. We pose it as a challenge to develop algorithms which can also certify the correctness of the equations we found for the higher dimensions.",

keywords = "Automated guessing, Computer algebra, Lattice walks",

author = "Manuel Kauers and Doron Zeilberger",

note = "Funding Information: E-mail addresses: mkauers@risc.jku.at (M. Kauers), zeilberg@math.rutgers.edu (D. Zeilberger). 1 Partially supported by the Austrian FWF grant Y464-N18. 2 Partially supported by the USA National Science Foundation.",

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AU - Zeilberger, Doron

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N2 - We present guesses, based on intensive computer algebra calculations, for recurrence equations of the sequences enumerating rook walks in up to twelve dimensions ending on the main diagonal. Computer proofs can in principle be constructed for all of them. For the moment, however, these computations are feasible only for low dimensions. We pose it as a challenge to develop algorithms which can also certify the correctness of the equations we found for the higher dimensions.

AB - We present guesses, based on intensive computer algebra calculations, for recurrence equations of the sequences enumerating rook walks in up to twelve dimensions ending on the main diagonal. Computer proofs can in principle be constructed for all of them. For the moment, however, these computations are feasible only for low dimensions. We pose it as a challenge to develop algorithms which can also certify the correctness of the equations we found for the higher dimensions.

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KW - Computer algebra

KW - Lattice walks

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