Minimal length maximal green sequences and triangulations of polygons

E. Cormier; P. Dillery; J. Resh; K. Serhiyenko; J. Whelan

doi:10.1007/s10801-016-0694-6

Minimal length maximal green sequences and triangulations of polygons

E. Cormier, P. Dillery, J. Resh, K. Serhiyenko, J. Whelan

Mathematics

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

7 Citations (SciVal)

Abstract

We use combinatorics of quivers and the corresponding surfaces to study maximal green sequences of minimal length for quivers of type A. We prove that such sequences have length n+ t, where n is the number of vertices and t is the number of 3-cycles in the quiver. Moreover, we develop a procedure that yields these minimal length maximal green sequences.

Original language	English
Pages (from-to)	905-930
Number of pages	26
Journal	Journal of Algebraic Combinatorics
Volume	44
Issue number	4
DOIs	https://doi.org/10.1007/s10801-016-0694-6
State	Published - Dec 1 2016

Bibliographical note

Funding Information:
This research was carried out at the University of Connecticut 2015 math REU funded by National Science Foundation under DMS-1262929. The fourth author was also supported by the National Science Foundation CAREER Grant DMS-1254567.

Publisher Copyright:
© 2016, Springer Science+Business Media New York.

Keywords

Cluster algebra
Maximal green sequence
Surface triangulation

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

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10.1007/s10801-016-0694-6

Cite this

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AU - Cormier, E.

AU - Dillery, P.

AU - Resh, J.

AU - Serhiyenko, K.

AU - Whelan, J.

N1 - Funding Information: This research was carried out at the University of Connecticut 2015 math REU funded by National Science Foundation under DMS-1262929. The fourth author was also supported by the National Science Foundation CAREER Grant DMS-1254567. Publisher Copyright: © 2016, Springer Science+Business Media New York.

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N2 - We use combinatorics of quivers and the corresponding surfaces to study maximal green sequences of minimal length for quivers of type A. We prove that such sequences have length n+ t, where n is the number of vertices and t is the number of 3-cycles in the quiver. Moreover, we develop a procedure that yields these minimal length maximal green sequences.

AB - We use combinatorics of quivers and the corresponding surfaces to study maximal green sequences of minimal length for quivers of type A. We prove that such sequences have length n+ t, where n is the number of vertices and t is the number of 3-cycles in the quiver. Moreover, we develop a procedure that yields these minimal length maximal green sequences.

KW - Cluster algebra

KW - Maximal green sequence

KW - Surface triangulation

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Minimal length maximal green sequences and triangulations of polygons

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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