Enumerating permutations avoiding a pair of Babson-Steingrimsson patterns
Journal article, 2005

Babson and Steingrimsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Subsequently, Claesson presented a complete solution for the number of permutations avoiding any single pattern of type (1, 2) or (2, 1). For eight of these twelve patterns the answer is given by the Bell numbers. For the remaining four the answer is given by the Catalan numbers. In the present paper we give a complete solution for the number of permutations avoiding a pair of patterns of type (1, 2) or (2, 1). We also conjecture the number of permutations avoiding the patterns in any set of three or more such patterns.

pattern avoidance

permutation

Author

Anders Claesson

Chalmers, Mathematical Sciences

University of Gothenburg

Toufik Mansour

Ars Combinatoria

0381-7032 (ISSN)

Vol. 77 17-31

Subject Categories

Mathematics

More information

Created

10/6/2017