A DECOMPOSITION OF THE SHARD INTERSECTION ORDER ON THE SYMMETRIC GROUP

作者: T. Kyle Petersen

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

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