Sciweavers

Share
COMBINATORICS
2006

Shift-Induced Dynamical Systems on Partitions and Compositions

8 years 11 months ago
Shift-Induced Dynamical Systems on Partitions and Compositions
The rules of "Bulgarian solitaire" are considered as an operation on the set of partitions to induce a finite dynamical system. We focus on partitions with no preimage under this operation, known as Garden of Eden points, and their relation to the partitions that are in cycles. These are the partitions of interest, as we show that starting from the Garden of Eden points leads through the entire dynamical system to all cycle partitions. A primary result concerns the number of Garden of Eden partitions (the number of cycle partitions is known from Brandt). The same operation and questions can be put in the context of compositions (ordered partitions), where we give stronger results.
Brian Hopkins, Michael A. Jones
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where COMBINATORICS
Authors Brian Hopkins, Michael A. Jones
Comments (0)
books