Geodesic
The 1-box pattern on pattern-avoiding permutations
Journal of integer sequences, Tome 17 (2014) no. 3
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.
Keywords: 1-box pattern, 132-avoiding permutation, separable permutation, Fibonacci number, pell number, distribution 
@article{JIS_2014__17_3_a1,
     author = {Kitaev,  Sergey and Remmel,  Jeffrey},
     title = {The 1-box pattern on pattern-avoiding permutations},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {3},
     zbl = {1328.05008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_3_a1/}
}
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Kitaev,  Sergey; Remmel,  Jeffrey. The 1-box pattern on pattern-avoiding permutations. Journal of integer sequences, Tome 17 (2014) no. 3. http://geodesic.mathdoc.fr/item/JIS_2014__17_3_a1/