Minimal length maximal green sequences and triangulations of polygons

Journal of Algebraic Combinatorics volume 44, pages 905–930 (2016)Cite this article

Abstract

We use combinatorics of quivers and the corresponding surfaces to study maximal green sequences of minimal length for quivers of type \(\mathbb {A}\). 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.

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Author information

Affiliations

  1. Department of Mathematics, Bowdoin College, Brunswick, ME, 04011, USA

    E. Cormier

  2. Department of Mathematics, University of Virginia, Charlottesville, VA, 22904-4137, USA

    P. Dillery

  3. Department of Mathematics, Roger Williams University, Bristol, RI, 02809, USA

    J. Resh

  4. Department of Mathematics, University of California, Berkeley, CA, 94720-3840, USA

    K. Serhiyenko

  5. Department of Mathematics, Vassar College, Poughkeepsie, NY, 12604, USA

    J. Whelan

Authors
  1. E. Cormier
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  2. P. Dillery
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  3. J. Resh
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  4. K. Serhiyenko
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  5. J. Whelan
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Corresponding author

Correspondence to K. Serhiyenko.

Additional 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.

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Cormier, E., Dillery, P., Resh, J. et al. Minimal length maximal green sequences and triangulations of polygons. J Algebr Comb 44, 905–930 (2016). https://doi.org/10.1007/s10801-016-0694-6

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Keywords

  • Maximal green sequence
  • Cluster algebra
  • Surface triangulation