Minimal length maximal green sequences

Alexander Garver; Thomas McConville; Khrystyna Serhiyenko

doi:10.1016/j.aam.2017.12.008

Minimal length maximal green sequences

Alexander Garver, Thomas McConville, Khrystyna Serhiyenko

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Maximal green sequences are important objects in representation theory, cluster algebras, and string theory. It is an open problem to determine what lengths are achieved by the maximal green sequences of a quiver. We combine the combinatorics of surface triangulations and the basics of scattering diagrams to address this problem. Our main result is a formula for the length of minimal length maximal green sequences of quivers defined by triangulations of an annulus or a punctured disk.

Original language	English
Pages (from-to)	76-138
Number of pages	63
Journal	Advances in Applied Mathematics
Volume	96
DOIs	https://doi.org/10.1016/j.aam.2017.12.008
State	Published - May 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Inc.

Keywords

Maximal green sequence
Quiver mutation
Scattering diagram
Triangulated surface

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aam.2017.12.008

Cite this

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title = "Minimal length maximal green sequences",

abstract = "Maximal green sequences are important objects in representation theory, cluster algebras, and string theory. It is an open problem to determine what lengths are achieved by the maximal green sequences of a quiver. We combine the combinatorics of surface triangulations and the basics of scattering diagrams to address this problem. Our main result is a formula for the length of minimal length maximal green sequences of quivers defined by triangulations of an annulus or a punctured disk.",

keywords = "Maximal green sequence, Quiver mutation, Scattering diagram, Triangulated surface",

author = "Alexander Garver and Thomas McConville and Khrystyna Serhiyenko",

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T1 - Minimal length maximal green sequences

AU - Garver, Alexander

AU - McConville, Thomas

AU - Serhiyenko, Khrystyna

PY - 2018/5

Y1 - 2018/5

N2 - Maximal green sequences are important objects in representation theory, cluster algebras, and string theory. It is an open problem to determine what lengths are achieved by the maximal green sequences of a quiver. We combine the combinatorics of surface triangulations and the basics of scattering diagrams to address this problem. Our main result is a formula for the length of minimal length maximal green sequences of quivers defined by triangulations of an annulus or a punctured disk.

AB - Maximal green sequences are important objects in representation theory, cluster algebras, and string theory. It is an open problem to determine what lengths are achieved by the maximal green sequences of a quiver. We combine the combinatorics of surface triangulations and the basics of scattering diagrams to address this problem. Our main result is a formula for the length of minimal length maximal green sequences of quivers defined by triangulations of an annulus or a punctured disk.

KW - Maximal green sequence

KW - Quiver mutation

KW - Scattering diagram

KW - Triangulated surface

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JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

ER -

Minimal length maximal green sequences

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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