The Number of Permutations Avoiding a Set of Generalized Permutation Patterns
Yonah Biers-Ariel
Department of Mathematics
Rutgers University
Piscataway, NJ 08854
USA
Abstract:
We prove a conjecture that the sequence defined recursively
by a1 = 1, a2 = 2,
an = 4an-1 - 2an-2 counts the number of length-n permutations
avoiding the four generalized permutation patterns 1-32-4, 1-42-3,
2-31-4, and 2-41-3.
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(Concerned with sequences
A006012.)
Received July 29 2017; revised version received August 29 2017.
Published in Journal of Integer Sequences, August 31 2017.
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