Sebastian A. Csar, Rik Sengupta, Warut Suksompong
Published 2011-08-29, updated 2013-09-15Version 2
We explore some of the properties of a subposet of the Tamari lattice introduced by Pallo, which we call the comb poset. We show that three binary functions that are not well-behaved in the Tamari lattice are remarkably well-behaved within an interval of the comb poset: rotation distance, meets and joins, and the common parse words function for a pair of trees. We relate this poset to a partial order on the symmetric group studied by Edelman.
Tamari lattices and noncrossing partitions in type B and beyond
Noncrossing Partitions, Tamari Lattices, and Parabolic Quotients of the Symmetric Group
A New Partial Order on SYT
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