The 1-Box Pattern on Pattern-Avoiding Permutations
Sergey Kitaev
Department of Computer and Information Sciences
University of Strathclyde
Glasgow G1 1XH
United Kingdom
Jeffrey Remmel
Department of Mathematics
University of California, San Diego
La Jolla, CA 92093-0112
USA
Abstract:
This paper is continuation of the study of the 1-box pattern in
permutations in- troduced previously by the authors. We derive a
two-variable generating function for the distribution of this pattern
on 132-avoiding permutations, and then study some of its coefficients
providing a link to the Fibonacci numbers. We also find the number of
separable permutations with two and three occurrences of the 1-box
pattern.
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(Concerned with sequence
A052542.)
Received September 22 2013;
revised version received February 11 2014.
Published in Journal of Integer Sequences, February 15 2014.
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