Permutations Containing and Avoiding 123 and 132 Patterns
Aaron Robertson
Abstract
We prove that the number of permutations which avoid 132-patterns and have exactly one 123-pattern equals (n-2)2(n-3). We then give a bijection onto the set of permutations which avoid 123-patterns and have exactly one 132-pattern. Finally, we show that the number of permutations which contain exactly one 123-pattern and exactly one 132-pattern is (n-3)(n-4)2(n-5).
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