A Combinatorial Approach to the Solitaire Game

David AVIS; Antoine DEZA; Shmuel ONN

A Combinatorial Approach to the Solitaire Game

David AVIS, Antoine DEZA, Shmuel ONN

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The classical game of peg solitaire has uncertain origins, but was certainly popular by the time of Louis XIV, and was described by Leibniz in 1710. One of the classical problems concerning peg solitaire is the feasibility issue. An early tool used to show the infeasibility of various peg games is the rule-of-three [Suremain de Missery 1841]. In the 1960s the description of the solitaire cone [Boardman and Conway] provides necessary conditions: valid inequalities over this cone, known as pagoda functions, were used to show the infeasibility of various peg games. In this paper, we recall these necessary conditions and present new developments: the lattice criterion, which generalizes the rule-of-three; and results on the strongest pagoda functions, the facets of the solitaire cone.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E83-A No.4 pp.656-661

Publication Date: 2000/04/25

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Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)

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David AVIS, Antoine DEZA, Shmuel ONN, "A Combinatorial Approach to the Solitaire Game" in IEICE TRANSACTIONS on Fundamentals, vol. E83-A, no. 4, pp. 656-661, April 2000, doi: .
Abstract: The classical game of peg solitaire has uncertain origins, but was certainly popular by the time of Louis XIV, and was described by Leibniz in 1710. One of the classical problems concerning peg solitaire is the feasibility issue. An early tool used to show the infeasibility of various peg games is the rule-of-three [Suremain de Missery 1841]. In the 1960s the description of the solitaire cone [Boardman and Conway] provides necessary conditions: valid inequalities over this cone, known as pagoda functions, were used to show the infeasibility of various peg games. In this paper, we recall these necessary conditions and present new developments: the lattice criterion, which generalizes the rule-of-three; and results on the strongest pagoda functions, the facets of the solitaire cone.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e83-a_4_656/_p

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@ARTICLE{e83-a_4_656,
author={David AVIS, Antoine DEZA, Shmuel ONN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Combinatorial Approach to the Solitaire Game},
year={2000},
volume={E83-A},
number={4},
pages={656-661},
abstract={The classical game of peg solitaire has uncertain origins, but was certainly popular by the time of Louis XIV, and was described by Leibniz in 1710. One of the classical problems concerning peg solitaire is the feasibility issue. An early tool used to show the infeasibility of various peg games is the rule-of-three [Suremain de Missery 1841]. In the 1960s the description of the solitaire cone [Boardman and Conway] provides necessary conditions: valid inequalities over this cone, known as pagoda functions, were used to show the infeasibility of various peg games. In this paper, we recall these necessary conditions and present new developments: the lattice criterion, which generalizes the rule-of-three; and results on the strongest pagoda functions, the facets of the solitaire cone.},
keywords={},
doi={},
ISSN={},
month={April},}

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TY - JOUR
TI - A Combinatorial Approach to the Solitaire Game
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 656
EP - 661
AU - David AVIS
AU - Antoine DEZA
AU - Shmuel ONN
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E83-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2000
AB - The classical game of peg solitaire has uncertain origins, but was certainly popular by the time of Louis XIV, and was described by Leibniz in 1710. One of the classical problems concerning peg solitaire is the feasibility issue. An early tool used to show the infeasibility of various peg games is the rule-of-three [Suremain de Missery 1841]. In the 1960s the description of the solitaire cone [Boardman and Conway] provides necessary conditions: valid inequalities over this cone, known as pagoda functions, were used to show the infeasibility of various peg games. In this paper, we recall these necessary conditions and present new developments: the lattice criterion, which generalizes the rule-of-three; and results on the strongest pagoda functions, the facets of the solitaire cone.
ER -