Catalan numbers and pattern restricted set partitions

نویسندگان

  • Toufik Mansour
  • Matthias Schork
  • Mark Shattuck
چکیده

Suppose π = π1π2 · · ·πn 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 Cn−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.

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عنوان ژورنال:
  • Discrete Mathematics

دوره 312  شماره 

صفحات  -

تاریخ انتشار 2012