Article ID Journal Published Year Pages File Type
4648248 Discrete Mathematics 2012 13 Pages PDF
Abstract

Suppose π=π1π2⋯πnπ=π1π2⋯πn is a partition of size nn, represented in its canonical sequential form. We show that the number of partitions of size nn so represented having no two adjacent letters the same and avoiding a single pattern of length five is given by the Catalan number Cn−1Cn−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.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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