This paper is a continuation of the systematic study of the distributions of simple marked mesh patterns initiated in . We study simple marked mesh patterns on 132-avoiding permutations. We derive generating functions for the number of occurrences of 4-parameter simple marked mesh patterns where only one parameter is allowed to be non-zero or a non-empty set. We show that specializations of such generating functions count a number of classical combinatorial sequences. Generating functions for the number of occurrences of 4-parameter simple marked mesh patterns where two or more of the parameters are allowed to be non-zero are studied in the upcoming paper .
|Number of pages||38|
|Journal||Pure Mathematics and Applications|
|Publication status||Published - 2012|
- permutation statistics
- marked mesh pattern
- Catalan numbers
- Fibonacci numbers