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Fibonacci Numbers, Reduced Decompositions, and 321=3412 Pattern Classes
Daniel Daly
Department of Mathematics, Southeast Missouri State University, One University Plaza, Cape Girardeau, Missouri 63701, USA
ddaly@semo.edu
Annals of Combinatorics 14 (1) pp.53-64 Springer, 2010
AMS Subject Classification: 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 classification via reduced decompositions. The results are extended to involutions in the above pattern classes using reduced ecompositions reproducing a result of Egge.
Keywords: permutation patterns, reduced decompositions, combinatorics, Fibonacci numbers

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