, Volume 31, Issue 3, pp 337–363 | Cite as

On a Subposet of the Tamari Lattice

  • Sebastian A. CsarEmail author
  • Rik Sengupta
  • Warut Suksompong


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.


Tamari lattice Poset Four Color Theorem Semilattice 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Sebastian A. Csar
    • 1
    Email author
  • Rik Sengupta
    • 2
  • Warut Suksompong
    • 2
  1. 1.School of MathematicsUniversity Of MinnesotaMinneapolisUSA
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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