  We consider an infinite graph G whose vertex set is the set of natural
numbers and adjacency depends solely on the difference between vertices. We
study the largest cardinality of a set of permutations of [n] any pair of which
differ somewhere in a pair of adjacent vertices of G and determine it
completely in an interesting special case. We give estimates for other cases
and compare the results in case of complementary graphs. We also explore the
close relationship between our problem and the concept of Shannon capacity
"within a given type".
