Authors: Henri Mühle ¹; Nathan Williams ²

• 1 Laboratoire d'informatique Algorithmique : Fondements et Applications
• 2 Laboratoire de combinatoire et d'informatique mathématique [Montréal]

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.