Exchangeable Hoeffding decompositions over finite sets: A combinatorial characterization and counterexamples

We study Hoeffding decomposable exchangeable sequences with values in a finite set D = { d 1 , … , d K } . We provide a new combinatorial characterization of Hoeffding decomposability and use this result to show that, for every K ≥ 3 , there exists a class of neither Pólya nor i.i.d. D -valued exchangeable sequences that are Hoeffding decomposable.