Abstract
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 a number of 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.
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Csar, S.A., Sengupta, R. & Suksompong, W. On a Subposet of the Tamari Lattice. Order 31, 337–363 (2014). https://doi.org/10.1007/s11083-013-9305-5
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DOI: https://doi.org/10.1007/s11083-013-9305-5