Aaron Robertson - Permutations Containing and Avoiding 123 and 132 Patterns

dmtcs:261 - Discrete Mathematics & Theoretical Computer Science, January 1, 1999, Vol. 3 no. 4 - https://doi.org/10.46298/dmtcs.261
Permutations Containing and Avoiding 123 and 132 PatternsArticle

Authors: Aaron Robertson 1

  • 1 Department of Mathematics [Hamilton NY]

We prove that the number of permutations which avoid 132-patterns and have exactly one 123-pattern, equals (n2)2n3, for n3. 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 (n3)(n4)2n5, for n5.


Volume: Vol. 3 no. 4
Published on: January 1, 1999
Imported on: March 26, 2015
Keywords: Patterns,Words,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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