Pattern Avoidance in Set Partitions

Details Pattern Avoidance in Set Partitions Pattern Avoidance in Set Partitions

2006-04-12

arxiv.org/abs/math/0604292v1

Mathematics

Combinatorics

15 pages, see related papers at http://www.math.msu.edu/~sagan

Scientific paper

The study of patterns in permutations in a very active area of current research. Klazar defined and studied an analogous notion of pattern for set partitions. We continue this work, finding exact formulas for the number of set partitions which avoid certain specific patterns. In particular, we enumerate and characterize those partitions avoiding any partition of a 3-element set. This allows us to conclude that the corresponding sequences are P-recursive. Finally, we define a second notion of pattern in a set partition, based on its restricted growth function. Related results are obtained for this new definition.

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