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.
|Number of pages||19|
|Journal||Journal of Integer Sequences|
|Publication status||Published - 15 Feb 2014|
- 1-box pattern
- pattern avoidance
- pattern avoiding permutation