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arXiv · 2009.05342

A Consecutive Lehmer Code for Parabolic Quotients of the Symmetric Group

Wenjie Fang·Henri Mühle·Jean-Christophe Novelli
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Abstract

In this article we define an encoding for parabolic permutations that distinguishes between parabolic $231$-avoiding permutations. We prove that the componentwise order on these codes realizes the parabolic Tamari lattice, and conclude a direct and simple proof that the parabolic Tamari lattice is isomorphic to a certain $\nu$-Tamari lattice, with an explicit bijection. Furthermore, we prove that this bijection is closely related to the map $\Theta$ used when the lattice isomorphism was first proved in (Ceballos, Fang and M\"uhle, 2020), settling an open problem therein.

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Wenjie Fang, Henri Mühle, Jean-Christophe Novelli. 2020-09-11. A Consecutive Lehmer Code for Parabolic Quotients of the Symmetric Group. https://doi.org/10.37236/10578

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