Geodesic
A consecutive Lehmer code for parabolic quotients of the symmetric group
Wenjie Fang ; Henri Mühle1 ; Jean-Christophe Novelli
1TU Dresden Institut für Algebra
The electronic journal of combinatorics, Tome 28 (2021) no. 3
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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 Mühle, 2020), settling an open problem therein.
DOI : 10.37236/10578
Classification : 05A19, 06B99
Mots-clés : symmetric group, Tamari lattice, parabolic quotient, Lehmer code

Wenjie Fang    ; Henri Mühle  1   ; Jean-Christophe Novelli 

1 TU Dresden Institut für Algebra 
@article{10_37236_10578,
     author = {Wenjie Fang and Henri M\"uhle and Jean-Christophe Novelli},
     title = {A consecutive {Lehmer} code for parabolic quotients of the symmetric group},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {3},
     doi = {10.37236/10578},
     zbl = {1483.05012},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10578/}
}
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Wenjie Fang; Henri Mühle; Jean-Christophe Novelli. A consecutive Lehmer code for parabolic quotients of the symmetric group. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/10578

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