Geodesic
On a Subposet of the Tamari Lattice
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

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We discuss some properties of a subposet of the Tamari lattice introduced by Pallo (1986), 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 (1989). 
@article{DMTCS_2012_special_263_a49,
     author = {Csar, Sebastian A. and Sengupta, Rik and Suksompong, Warut},
     title = {On a {Subposet} of the {Tamari} {Lattice}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     year = {2012},
     doi = {10.46298/dmtcs.3063},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3063/}
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Csar, Sebastian A.; Sengupta, Rik; Suksompong, Warut. On a Subposet of the Tamari Lattice. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi : 10.46298/dmtcs.3063. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3063/

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