Geodesic
Shift-induced dynamical systems on partitions and compositions
The electronic journal of combinatorics, Tome 13 (2006)
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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.
DOI : 10.37236/1106
Classification : 05A17, 37B10
Mots-clés : Garden of Eden points, number of Garden of Eden partitions, ordered partitions 
@article{10_37236_1106,
     author = {Brian Hopkins and Michael A. Jones},
     title = {Shift-induced dynamical systems on partitions and compositions},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1106},
     zbl = {1115.05006},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1106/}
}
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%A Michael A. Jones
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Brian Hopkins; Michael A. Jones. Shift-induced dynamical systems on partitions and compositions. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1106

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