Pattern avoidance in "flattened" partitions

Details Pattern avoidance in "flattened" partitions Pattern avoidance in "flattened" partitions

2008-02-15

arxiv.org/abs/0802.2275v1

Mathematics

Combinatorics

8 pages

Scientific paper

To flatten a set partition (with apologies to Mathematica) means to form a permutation by erasing the dividers between its blocks. Of course, the result depends on how the blocks are listed. For the usual listing--increasing entries in each block and blocks arranged in increasing order of their first entries--we count the partitions of [n] whose flattening avoids a single 3-letter pattern. Five counting sequences arise: a null sequence, the powers of 2, the Fibonacci numbers, the Catalan numbers, and the binomial transform of the Catalan numbers.

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