The 1-box pattern on pattern-avoiding permutations

Kitaev, Sergey and Remmel, Jeffrey (2014) The 1-box pattern on pattern-avoiding permutations. Journal of Integer Sequences, 17 (3).

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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.