ALGEBRAIC COMBINATORICS

no. 4
Trimming the permutahedron to extend the parking space
Konvalinka, Matjaž1; Sulzgruber, Robin2; Tewari, Vasu3
1 University of Ljubljana & Institute of Mathematics, Physics and Mechanics Department of Mathematics Ljubljana Slovenia
2 York University Department of Mathematics and Statistics Toronto Canada
3 University of Hawaii at Manoa Department of Mathematics Honolulu HI 96822, USA
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: 10.5802/alco.173
Classification: 05E05, 05E10, 05A15, 05A19, 20C30, 05E18
Keywords: $h$-positivity, Lyndon word, parking function, permutahedron.
Konvalinka, Matjaž 1; Sulzgruber, Robin 2; Tewari, Vasu 3

1 University of Ljubljana & Institute of Mathematics, Physics and Mechanics Department of Mathematics Ljubljana Slovenia
2 York University Department of Mathematics and Statistics Toronto Canada
3 University of Hawaii at Manoa Department of Mathematics Honolulu HI 96822, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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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