\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
%\def\frac#1 #2 {{#1\over #2}}
\def\emph#1{{\it #1}}
\def\em{\it}
\nopagenumbers
\noindent
%
%
{\bf Brian Hopkins and Michael A. Jones}
%
%
\medskip
\noindent
%
%
{\bf Shift-Induced Dynamical Systems on Partitions and Compositions}
%
%
\vskip 5mm
\noindent
%
%
%
%
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.
\bye