Abstract
Some permutation patterns have been studied with a view to generating some recursion relations and generating functions for enumerating the number of subwords arising from the patterns. This was achieved using some prime generating functions. Furthermore, a comprehensive counting scheme was established for the patterns based upon the length of the emerging subwords. In addition, some group and graph theoretic consequences of these patterns were identified. This report highlights an important relationship between some important algebraic schemes; permutation patterns and groups on the one hand and the counting theory and integer sequences on the other.
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