A Finiteness Theorem in Algebraic Statistics

The set of all non-negative integer pxq-tables with fixed row sums and column sums can be connected by local moves involving changes in 2x2-subtables in each step. The difficult question of finding analogous moves for random walks on higher-dimensional contingency tables arises in statistics. Aoki and Takemura proved recently that 3x3xr-tables can be connected by moves of format 3x3x5, and they conjectured a similar finiteness theorem for pxqxr-tables when p and q are fixed and r increases. In this talk we prove their conjecture, by developing a general theory of higher Lawrence polytopes.

Joint work with Francisco Santos (math.CO/0209326)