Generalized Fréchet Bounds for Cell Entries in Multidimensional Contingency Tables Special Volume in honor of memory of S.E.Fienberg Contingency table FKG inequality Fréchet bounds log-supermodular function total positivity. We consider the lattice, L, of all subsets of a multidimensional contingency table and establish the properties of monotonicity and supermodularity for the marginalization function, n(·), on L. We derive from the supermodularity of n(·) some generalized Fr ́echet inequalities comple- menting and extending inequalities of Dobra and Fienberg. Further, we construct new monotonic and supermodular functions from n(·), and we remark on the connection between supermodularity and some correlation inequalities for probability distributions on lattices. We also apply an inequal- ity of Ky Fan to derive a new approach to Fr ́echet inequalities for multidimensional contingency tables. Richards, Donald Uhler, Caroline Article application/pdf islandora:1009723 http://hdl.handle.net/10560/islandora:1009723 MATH / Applied Mathematics Illinois Institute of Technology Journal of Algebraic Statistics en Open Access