Abstract | ||
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The Grundy number of an impartial game G is the size of the unique Nim heap equal to G. We introduce a new variant of Nim, Restricted Nim, which restricts the number of stones a player may remove from a heap in terms of the size of the heap. Certain classes of Restricted Nim are found to produce sequences of Grundy numbers with a self-similar fractal structure. Extending work of C. Kimberling, we obtain new characterizations of these "fractal sequences" and give a bijection between these sequences and certain upper-triangular arrays. As a special case we obtain the game of Serial Nim, in which the Nim heaps are ordered from left to right, and players can move only in the leftmost nonempty heap. |
Year | Venue | Field |
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2006 | ARS COMBINATORIA | Grundy's game,Discrete mathematics,Combinatorics,Bijection,Grundy number,Fractal,Heap (data structure),Mathematics,Special case,Nimber |
DocType | Volume | ISSN |
Journal | 80 | 0381-7032 |
Citations | PageRank | References |
1 | 0.43 | 5 |
Authors | ||
1 |
Name | Order | Citations | PageRank |
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Lionel Levine | 1 | 31 | 5.43 |