Numerical and Symbolic Studies of the Peaceable Queens Problem

Yukun Yao; Doron Zeilberger

doi:10.1080/10586458.2019.1616338

Numerical and Symbolic Studies of the Peaceable Queens Problem

Yukun Yao, Doron Zeilberger

School of Arts and Sciences, Mathematics

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

Abstract

We discuss, and make partial progress on, the peaceable queens problem, the protagonist of OEIS sequence A250000. Symbolically, we prove that Jubin’s construction of two pentagons is at least a local optimum. Numerically, we find the exact numerical optimums for some specific configurations. Our method can be easily applied to more complicated configurations with more parameters.

Original language	English (US)
Pages (from-to)	269-279
Number of pages	11
Journal	Experimental Mathematics
Volume	31
Issue number	1
DOIs	https://doi.org/10.1080/10586458.2019.1616338
State	Published - 2022

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

05A15
OEIS
combinatorics
experimental mathematics
peaceable queens

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10.1080/10586458.2019.1616338

Cite this

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title = "Numerical and Symbolic Studies of the Peaceable Queens Problem",

abstract = "We discuss, and make partial progress on, the peaceable queens problem, the protagonist of OEIS sequence A250000. Symbolically, we prove that Jubin{\textquoteright}s construction of two pentagons is at least a local optimum. Numerically, we find the exact numerical optimums for some specific configurations. Our method can be easily applied to more complicated configurations with more parameters.",

keywords = "05A15, OEIS, combinatorics, experimental mathematics, peaceable queens",

author = "Yukun Yao and Doron Zeilberger",

note = "Funding Information: We are thankful to Neil J.A. Sloane for introducing us to this interesting problem and we are also grateful to Lun Zhang for pleasant conversations and helpful remarks. We sincerely thank the anonymous referee for careful review and useful suggestions. We appreciate Shalosh B. Ekhad{\textquoteright}s impeccable computing support. Publisher Copyright: {\textcopyright} 2019 Taylor & Francis Group, LLC.",

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N1 - Funding Information: We are thankful to Neil J.A. Sloane for introducing us to this interesting problem and we are also grateful to Lun Zhang for pleasant conversations and helpful remarks. We sincerely thank the anonymous referee for careful review and useful suggestions. We appreciate Shalosh B. Ekhad’s impeccable computing support. Publisher Copyright: © 2019 Taylor & Francis Group, LLC.

PY - 2022

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AB - We discuss, and make partial progress on, the peaceable queens problem, the protagonist of OEIS sequence A250000. Symbolically, we prove that Jubin’s construction of two pentagons is at least a local optimum. Numerically, we find the exact numerical optimums for some specific configurations. Our method can be easily applied to more complicated configurations with more parameters.

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Numerical and Symbolic Studies of the Peaceable Queens Problem

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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