Information Theory: Coding Theorems for Discrete Memoryless Systems
Information Theory: Coding Theorems for Discrete Memoryless Systems
Pairwise colliding permutations and the capacity of infinite graphs
SIAM Journal on Discrete Mathematics
SIAM Journal on Discrete Mathematics
On the Shannon capacity of a graph
IEEE Transactions on Information Theory
Permutation Capacities of Families of Oriented Infinite Paths
SIAM Journal on Discrete Mathematics
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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.''