Fractal Sequences and Restricted Nim

Details Fractal Sequences and Restricted Nim Fractal Sequences and Restricted Nim

2004-09-21

arxiv.org/abs/math/0409408v1

Mathematics

Combinatorics

15 pages, to appear in Ars Combinatoria

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Fractal Sequences and Restricted Nim does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fractal Sequences and Restricted Nim, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fractal Sequences and Restricted Nim will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-328001