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

Research Institute for Symbolic Computation

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

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
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
Publication status	Published - Oct 2011

Fields of science

101001 Algebra
101002 Analysis
101 Mathematics
102 Computer Sciences
102011 Formal languages
101009 Geometry
101013 Mathematical logic
101020 Technical mathematics
101025 Number theory
101012 Combinatorics
101005 Computer algebra
101006 Differential geometry
101003 Applied geometry
102025 Distributed systems

JKU Focus areas

Computation in Informatics and Mathematics

Access to Document

10.1016/j.aam.2011.03.004

Cite this

@article{470d43ee14ea4120b487affd0ef073f5,

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.",

author = "Manuel Kauers and Doron Zeilberger",

year = "2011",

month = oct,

doi = "10.1016/j.aam.2011.03.004",

language = "English",

volume = "47",

pages = "813--819",

journal = "Advances in Applied Mathematics",

issn = "0196-8858",

publisher = "Elsevier",

number = "4",

}

TY - JOUR

T1 - The computational challenge of enumerating high-dimensional rook walks

AU - Kauers, Manuel

AU - Zeilberger, Doron

PY - 2011/10

Y1 - 2011/10

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.

UR - https://www.scopus.com/pages/publications/80052481294

U2 - 10.1016/j.aam.2011.03.004

DO - 10.1016/j.aam.2011.03.004

M3 - Article

SN - 0196-8858

VL - 47

SP - 813

EP - 819

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 4

ER -

The computational challenge of enumerating high-dimensional rook walks

Abstract

Fields of science

JKU Focus areas

Access to Document

Other files and links

Cite this