# Minimal length maximal green sequences and triangulations of polygons

## 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

Authors

### Corresponding author

Correspondence to K. Serhiyenko.

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