Arrays, numeration systems and Frankenstein games

We define an infinite array A of nonnegative integers based on a linear recurrence, whose second row provides basis elements of an exotic ternary numeration system. Using the numeration system we explore many properties of A . Further, we propose and analyze a family Frankenstein of 2-player pebblin...

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Bibliographic Details
Published inTheoretical computer science Vol. 282; no. 2; pp. 271 - 284
Main Author Fraenkel, Aviezri S.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Amsterdam Elsevier B.V 10.06.2002
Elsevier
Subjects
Algebra
Algebraic geometry
Applied sciences
Combinatorial games
Complexity
Exact sciences and technology
Game theory
Mathematics
Matrices
Numeration systems
Operational research and scientific management
Operational research. Management science
Sciences and techniques of general use
Combinatorial games
Numeration systems
Matrices
Complexity
Player strategy
Matrix algebra
Game theory
Numeration system
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Summary:We define an infinite array A of nonnegative integers based on a linear recurrence, whose second row provides basis elements of an exotic ternary numeration system. Using the numeration system we explore many properties of A . Further, we propose and analyze a family Frankenstein of 2-player pebbling games played on a semi-infinite strip, and present a winning strategy based on certain subarrays of A . Though the strategy looks easy, it is actually computationally hard. The numeration system is then used to decide whether the family has an efficient strategy or not.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0304-3975
1879-2294
DOI:10.1016/S0304-3975(01)00070-6