\BOOKMARK [1][-]{section.1}{Introduction}{}% 1
\BOOKMARK [1][-]{section.2}{Binary fusion}{}% 2
\BOOKMARK [2][-]{subsection.2.1}{Number of ways to play}{section.2}% 3
\BOOKMARK [3][-]{subsubsection.2.1.1}{The recursion}{subsection.2.1}% 4
\BOOKMARK [3][-]{subsubsection.2.1.2}{General formula}{subsection.2.1}% 5
\BOOKMARK [3][-]{subsubsection.2.1.3}{Bijective proof}{subsection.2.1}% 6
\BOOKMARK [2][-]{subsection.2.2}{Total number of paths}{section.2}% 7
\BOOKMARK [2][-]{subsection.2.3}{Total number of edges and states}{section.2}% 8
\BOOKMARK [1][-]{section.3}{Refining partitions: the game over Z}{}% 9
\BOOKMARK [1][-]{section.4}{Playing in modulo 3}{}% 10
\BOOKMARK [2][-]{subsection.4.1}{Number of ways to play}{section.4}% 11
\BOOKMARK [2][-]{subsection.4.2}{Total number of edges and states}{section.4}% 12
\BOOKMARK [1][-]{section.5}{Number of ways to play over polynomial rings over Z/2Z}{}% 13
\BOOKMARK [1][-]{section.6}{Acknowledgments}{}% 14