Title of article :
Catalan numbers and pattern restricted set partitions
Author/Authors :
Mansour، نويسنده , , Toufik and Schork، نويسنده , , Matthias and Shattuck، نويسنده , , Mark، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2012
Abstract :
Suppose π = π 1 π 2 ⋯ π n is a partition of size n , represented in its canonical sequential form. We show that the number of partitions of size n so represented having no two adjacent letters the same and avoiding a single pattern of length five is given by the Catalan number C n − 1 in six particular instances. In addition to supplying apparently new combinatorial structures counted by the Catalan numbers, this provides interesting examples of the more general question of enumerating how many members which belong to some class of words satisfying an adjacency requirement avoid a given subsequence pattern.
Keywords :
Catalan number , Pattern avoidance , set partition
Journal title :
Discrete Mathematics
Journal title :
Discrete Mathematics