c Birkhauser Verlag, Basel, 2010 Annals of Combinatorics Fibonacci Numbers, Reduced Decompositions, and 321=3412 Pattern Classes

AMS Subject Classication: 05 Abstract. We provide a bijection between the permutations in Sn that avoid 3412 and contain exactly one 321 pattern with the permutations in Sn+1 that avoid 321 and contain exactly one 3412 pattern. The enumeration of these classes is obtained from their classication via reduced decompositions. The results are extended to involutions in the above pattern classes using reduced decompositions reproducing a result of Egge