Sebastian A. Csar ; Rik Sengupta ; Warut Suksompong - On a Subposet of the Tamari Lattice

dmtcs:3063 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) - https://doi.org/10.46298/dmtcs.3063
On a Subposet of the Tamari LatticeArticle

Authors: Sebastian A. Csar 1; Rik Sengupta 2; Warut Suksompong 3

  • 1 School of Mathematics
  • 2 Department of Mathematics - Princeton University
  • 3 Department of Mathematics [MIT]

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).

https://doi.org/10.46298/dmtcs.3063
Source: HAL:hal-01283111v1
Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Imported on: January 31, 2017
Keywords: tree rotation,poset, Tamari lattice,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Reflection Group Combinatorics; Funder: National Science Foundation; Code: 1001933

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