Compact representations of the intersection structure of families of finite sets

The Nesetril-Pultr dimension of the Kneser graph is interpreted as the shor test length of strings over an infinite alphabet representing the vertices of the graph so that the absence of coincidences in the codewords of a pair of vertices is equivalent to adjacency, i.e., to the two underlying sets b eing disjoint. We study analogous but more demanding representations in cas e the alphabet size may be limited and yet the full intersection has to be determined from the coincidences. Our results introduce a connection betwee n extremal set theory and zero-error problems in multiterminal source codin g in the Shannon sense.