A decomposition of the shard intersection order on the symmetric group

Details A decomposition of the shard intersection order on the symmetric group A decomposition of the shard intersection order on the symmetric group

2011-08-29

arxiv.org/abs/1108.5761v1

Mathematics

Combinatorics

16 pages, several figures

Scientific paper

Inspired by work of Simion and Ullman on the lattice of noncrossing partitions, we show that the shard intersection order on the symmetric group admits a \emph{symmetric boolean decomposition}, i.e., a partition into disjoint boolean algebras whose middle ranks coincide with the middle rank of the poset. Our decomposition also yields a new symmetric boolean decomposition of the noncrossing partition lattice.

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