• Hochschild polytopes

Treffer: Hochschild polytopes

Title:
Hochschild polytopes
Authors:
Vincent Pilaud, Daria Poliakova
Contributors:
Centre National de la Recherche Scientifique (CNRS), Laboratoire d'informatique de l'École polytechnique Palaiseau (LIX), École polytechnique (X), Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Centre National de la Recherche Scientifique (CNRS), University of Southern Denmark (SDU), VP was partially supported by the French grant CHARMS (ANR-19-CE40-0017), and by the French–Austrian projects PAGCAP (ANR-21-CE48-0020 & FWF I 5788). DP was partially supported by the Danish National Research Foundation grant DNRF157., ANR-19-CE40-0017,CHARMS,Amas, Algèbre Homologique, Représentations et Symétrie Miroir(2019), ANR-21-CE48-0020,PAGCAP,Au delà du Permutoèdre et de l'Associaèdre : Géométrie, Combinatoire, Algèbre et Probabilité(2021)
Source:
Mathematische Annalen. 392:2395-2441
Publication Status:
Preprint
Publisher Information:
Springer Science and Business Media LLC, 2025.
Publication Year:
2025
Subject Terms:
Hochschild lattice, 52B11, 52B12, 52B11, 52B12, 05A15, 05E99, 06B10, Freehedron, Quotient, Combinatorics, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], Multiplihedron, FOS: Mathematics, Combinatorics (math.CO), 05A15, 05E99, 06B10
Document Type:
Fachzeitschrift Article<br />Conference object<br />Report
Language:
English
ISSN:
1432-1807
0025-5831
DOI:
10.1007/s00208-025-03120-x
DOI:
10.48550/arxiv.2307.05940
Access URL:
http://arxiv.org/abs/2307.05940
https://portal.findresearcher.sdu.dk/da/publications/b2f43931-94b4-4336-bcfe-f3ace0295fb7
Rights:
CC BY
arXiv Non-Exclusive Distribution
read_only
Accession Number:
edsair.doi.dedup.....fff57f5f1a7fdcf3beffb058e3a51f83
Database:
OpenAIRE

Weitere Informationen

The (m, n)-multiplihedron is a polytope whose faces correspond to m-painted n-trees, and whose oriented skeleton is the Hasse diagram of the rotation lattice on binary m-painted n-trees. Deleting certain inequalities from the facet description of the (m, n)-multiplihedron, we construct the (m, n)-Hochschild polytope whose faces correspond to m-lighted n-shades, and whose oriented skeleton is the Hasse diagram of the rotation lattice on unary m-lighted n-shades. Moreover, there is a natural shadow map from m-painted n-trees to m-lighted n-shades, which turns out to define a meet semilattice morphism of rotation lattices. In particular, when $$m=1$$ m = 1 , our Hochschild polytope is a deformed permutahedron whose oriented skeleton is the Hasse diagram of the Hochschild lattice.