Meet and join within the lattice of set partitions.

Canfield, Rodney E.

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On noncrossing and nonnesting partitions for classical reflection groups.

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Records in set partitions.

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On partitions avoiding 3-crossings.

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Counting set systems by weight.

Klazar, Martin (2005)

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On colored set partitions of type B n

David Wang (2014)

Open Mathematics

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Generalizing Reiner’s notion of set partitions of type B n, we define colored B n-partitions by coloring the elements in and not in the zero-block respectively. Considering the generating function of colored B n-partitions, we get the exact formulas for the expectation and variance of the number of non-zero-blocks in a random colored B n-partition. We find an asymptotic expression of the total number of colored B n-partitions up to an error of O(n −1/2log7/2 n], and prove that the centralized...