Fractal Sequences and Restricted Nim
| dc.creator | Levine, Lionel | |
| dc.date | 2004-09-21 | |
| dc.date.accessioned | 2026-07-07T05:12:27Z | |
| dc.date.available | 2026-07-07T05:12:27Z | |
| dc.description | 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. | |
| dc.description | 15 pages, to appear in Ars Combinatoria | |
| dc.identifier | https://arxiv.org/abs/math/0409408 | |
| dc.identifier | http://arxiv.org/abs/math/0409408 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72577 | |
| dc.subject | Combinatorics | |
| dc.title | Fractal Sequences and Restricted Nim | |
| dc.type | text |