The 1-box pattern on pattern avoiding permutations

2013/05/29 by Sergey Kitaev, Kitaev, Sergey, Jeffrey Remmel +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1305.6970

arxiv created 2013/05/29 · arxiv updated 2013/05/31

Abstract

This paper is continuation of the study of the 1-box pattern in permutations introduced by the authors in \citekitrem4. 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.

Related

• Permutations avoiding a nonconsecutive instance of a 2- or 3-letter pattern
• Counting Permutations that Avoid Many Patterns
• Patterns and Fractions
• Counting occurrences of a pattern of type (1,2) or (2,1) in permutations
• Permutations Containing and Avoiding 123 and 132 Patterns