Journal of Integer Sequences, Vol. 10 (2007), Article 07.6.4

Enumerating Permutations Avoiding More Than Three Babson-Steingrímsson Patterns

Antonio Bernini and Elisa Pergola
Dipartimento di Sistemi e Informatica
Università di Firenze
viale G. B. Morgagni 65
50134 Firenze


Claesson and Mansour recently proposed some conjectures about the enumeration of the permutations avoiding more than three Babson-Steingrímsson patterns (generalized patterns of type (1,2) or (2,1)). The avoidance of one, two or three patterns has already been considered. Here, the cases of four and five forbidden patterns are solved and the exact enumeration of the permutations avoiding them is given, confirming the conjectures of Claesson and Mansour. The approach we use can be easily extended to the cases of more than five forbidden patterns.

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(Concerned with sequences A000027 A000045 A000079 A000124 A001405 and A094373 .)

Received April 27 2007; revised version received June 11 2007. Published in Journal of Integer Sequences, June 11 2007.

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