Discrete Mathematics & Theoretical Computer Science
Volume 3 n° 4 (1999), pp. 151-154
author: | Aaron Robertson |
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title: | Permutations Containing and Avoiding 123 and 132 Patterns |
keywords: | Patterns, Words |
abstract: | We prove that the number of permutations which avoid 132-patterns and have exactly one 123-pattern, equals (n-2)2^{n-3}, for 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}, for n>=5. |
reference: | Aaron Robertson (1999), Permutations Containing and Avoiding 123 and 132 Patterns, Discrete Mathematics and Theoretical Computer Science 3, pp. 151-154 |
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Automatically produced on Mon Nov 15 13:59:56 CET 1999 by novelli