Restricted permutations by patterns of type $(2,1)$

Details Restricted permutations by patterns of type $(2,1)$ Restricted permutations by patterns of type $(2,1)$

2002-02-21

arxiv.org/abs/math/0202219v1

Mathematics

Combinatorics

19 pages

Scientific paper

Recently, Babson and Steingrimsson (see \cite{BS}) introduced generalized permutations patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. In this paper we study the generating functions for the number of permutations on $n$ letters avoiding a generalized pattern $ab\mn c$ where $(a,b,c)\in S_3$, and containing a prescribed number of occurrences of generalized pattern $cd\mn e$ where $(c,d,e)\in S_3$. As a consequence, we derive all the previously known results for this kind of problems, as well as many new results.

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