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 In I 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." (C) 2008 Elsevier Inc. All rights reserved.
On types of growth for graph-different permutations / Korner, Janos; Simonyi, Gabor; Sinaimeri, Blerina. - In: JOURNAL OF COMBINATORIAL THEORY. SERIES A. - ISSN 0097-3165. - 116:3(2009), pp. 713-723. [10.1016/j.jcta.2008.11.003]
On types of growth for graph-different permutations
Blerina Sinaimeri
2009
Abstract
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 In I 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." (C) 2008 Elsevier Inc. All rights reserved.
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