# ALGEBRAIC COMBINATORICS

Trimming the permutahedron to extend the parking space
Algebraic Combinatorics, Volume 4 (2021) no. 4, pp. 663-674.

Berget and Rhoades asked whether the permutation representation obtained by the action of ${S}_{n-1}$ on parking functions of length $n-1$ can be extended to a permutation action of ${S}_{n}$. We answer this question in the affirmative. We realize our module in two different ways. The first description involves binary Lyndon words and the second involves the action of the symmetric group on the lattice points of the trimmed standard permutahedron.

Received:
Revised:
Accepted:
Published online:
DOI: https://doi.org/10.5802/alco.173
Classification: 05E05,  05E10,  05A15,  05A19,  20C30,  05E18
Keywords: $h$-positivity, Lyndon word, parking function, permutahedron.
@article{ALCO_2021__4_4_663_0,
author = {Konvalinka, Matja\v{z} and Sulzgruber, Robin and Tewari, Vasu},
title = {Trimming the permutahedron to extend the parking space},
journal = {Algebraic Combinatorics},
pages = {663--674},
publisher = {MathOA foundation},
volume = {4},
number = {4},
year = {2021},
doi = {10.5802/alco.173},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.173/}
}
Konvalinka, Matjaž; Sulzgruber, Robin; Tewari, Vasu. Trimming the permutahedron to extend the parking space. Algebraic Combinatorics, Volume 4 (2021) no. 4, pp. 663-674. doi : 10.5802/alco.173. https://alco.centre-mersenne.org/articles/10.5802/alco.173/

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