Local distributions for eigenfunctions and for perfect colorings of   q-ary hypercube
  Under study are the eigenfunctions and perfect colorings of the graph of $n$-dimensional $q$-ary Hamming space. We obtain the interdependence of local distributions of an eigenfunction in two orthogonal faces. We prove also an analogous result for perfect colorings. 
Anastasia Vasil'eva
math.CO