Stokes posets and serpent nests

30 pages, 12 figures We study two different objects attached to an arbitrary quadrangulation of a regular polygon. The first one is a poset, closely related to the Stokes polytopes introduced by Baryshnikov. The second one is a set of some paths configurations inside the quadrangulation, satisfying...

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Published in:Discrete Mathematics and Theoretical Computer Science Vol. 18 no. 3; no. Combinatorics; p. Q1
Main Author: Chapoton, Frédéric
Format: Journal Article
Language:English
Published: Nancy DMTCS 02.12.2016
Discrete Mathematics & Theoretical Computer Science
Subjects:
[math.math-co] mathematics [math]/combinatorics [math.co]
[math.math-qa] mathematics [math]/quantum algebra [math.qa]
[math.math-rt] mathematics [math]/representation theory [math.rt]
Combinatorial analysis
Combinatorics
Fuzzy sets
Lattice theory
Mathematical research
Mathematics
msc: 05e 06a11 13f60
Polygons
Polytopes
poset
quadrangulation
Quantum Algebra
Representation Theory
Set theory
tamari lattice
quadrangulation
Tamari lattice
poset
ISSN:1365-8050, 1462-7264, 1365-8050
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Abstract 30 pages, 12 figures We study two different objects attached to an arbitrary quadrangulation of a regular polygon. The first one is a poset, closely related to the Stokes polytopes introduced by Baryshnikov. The second one is a set of some paths configurations inside the quadrangulation, satisfying some specific constraints. These objects provide a generalisation of the existing combinatorics of cluster algebras and nonnesting partitions of type A. On étudie deux objets attachés à une quadrangulation quelconque d'un polygone régulier. Le premier objet est un ensemble partiellement ordonné, fortement lié aux polytopes de Stokes introduits par Barysknikov. Le second est un ensemble de configurations de chemins dans la quadrangulation. Ces deux objets généralisent respectivement les aspects combinatoires des algèbres amassées et des partitions non-emboitées de type A.
AbstractList We study two different objects attached to an arbitrary quadrangulation of a regular polygon. The first one is a poset, closely related to the Stokes polytopes introduced by Baryshnikov. The second one is a set of some paths configurations inside the quadrangulation, satisfying some specific constraints. These objects provide a generalisation of the existing combinatorics of cluster algebras and nonnesting partitions of type A. On étudie deux objets attachés à une quadrangulation quelconque d'un polygone régulier. Le premier objet est un ensemble partiellement ordonné, fortement lié aux polytopes de Stokes introduits par Barysknikov. Le second est un ensemble de configurations de chemins dans la quadrangulation. Ces deux objets généralisent respectivement les aspects combinatoires des algèbres amassées et des partitions non-emboitées de type A.
We study two different objects attached to an arbitrary quadrangulation of a regular polygon. The first one is a poset, closely related to the Stokes polytopes introduced by Baryshnikov. The second one is a set of some paths configurations inside the quadrangulation, satisfying some specific constraints. These objects provide a generalisation of the existing combinatorics of cluster algebras and nonnesting partitions of type A.
30 pages, 12 figures We study two different objects attached to an arbitrary quadrangulation of a regular polygon. The first one is a poset, closely related to the Stokes polytopes introduced by Baryshnikov. The second one is a set of some paths configurations inside the quadrangulation, satisfying some specific constraints. These objects provide a generalisation of the existing combinatorics of cluster algebras and nonnesting partitions of type A. On étudie deux objets attachés à une quadrangulation quelconque d'un polygone régulier. Le premier objet est un ensemble partiellement ordonné, fortement lié aux polytopes de Stokes introduits par Barysknikov. Le second est un ensemble de configurations de chemins dans la quadrangulation. Ces deux objets généralisent respectivement les aspects combinatoires des algèbres amassées et des partitions non-emboitées de type A.
30 pages, 12 figures
Audience Academic
Author Chapoton, Frédéric
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Snippet 30 pages, 12 figures We study two different objects attached to an arbitrary quadrangulation of a regular polygon. The first one is a poset, closely related to...
We study two different objects attached to an arbitrary quadrangulation of a regular polygon. The first one is a poset, closely related to the Stokes polytopes...
30 pages, 12 figures
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SubjectTerms [math.math-co] mathematics [math]/combinatorics [math.co]
[math.math-qa] mathematics [math]/quantum algebra [math.qa]
[math.math-rt] mathematics [math]/representation theory [math.rt]
Combinatorial analysis
Combinatorics
Fuzzy sets
Lattice theory
Mathematical research
Mathematics
msc: 05e 06a11 13f60
Polygons
Polytopes
poset
quadrangulation
Quantum Algebra
Representation Theory
Set theory
tamari lattice
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