Mühle, Henri and Williams, Nathan - Tamari Lattices for Parabolic Quotients of the Symmetric Group

dmtcs:2534 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Tamari Lattices for Parabolic Quotients of the Symmetric Group

Authors: Mühle, Henri and Williams, Nathan

We present a generalization of the Tamari lattice to parabolic quotients of the symmetric group. More precisely, we generalize the notions of 231-avoiding permutations, noncrossing set partitions, and nonnesting set partitions to parabolic quotients, and show bijectively that these sets are equinumerous. Furthermore, the restriction of weak order on the parabolic quotient to the parabolic 231-avoiding permutations is a lattice quotient. Lastly, we suggest how to extend these constructions to all Coxeter groups.


Source : oai:HAL:hal-01337754v1
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Submitted on: November 21, 2016
Keywords: Symmetric group,Parabolic quotients,Tamari lattice,Noncrossing partitions,Nonnesting partitions,Aligned elements,231-avoiding permutations,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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