Permutations Containing and Avoiding 123 and 132 Patterns

Details Permutations Containing and Avoiding 123 and 132 Patterns Permutations Containing and Avoiding 123 and 132 Patterns

1999-03-29

arxiv.org/abs/math/9903169v1

Mathematics

Combinatorics

5 pages

Scientific paper

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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