Geodesic
Combinatorial cluster expansion formulas from triangulated surfaces
Toshiya Yurikusa1
1Nagoya University
The electronic journal of combinatorics, Tome 26 (2019) no. 2
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We give a cluster expansion formula for cluster algebras with principal coefficients defined from triangulated surfaces in terms of maximal independent sets of angles. Our formula simplifies the cluster expansion formula given by Musiker, Schiffler and Williams in terms of perfect matchings of snake graphs. A key point of our proof is to give a bijection between maximal independent sets of angles in some triangulated polygon and perfect matchings of the corresponding snake graph. Moreover, they also correspond bijectively with perfect matchings of the corresponding bipartite graph and minimal cuts of the corresponding quiver with potential.
DOI : 10.37236/8351
Classification : 13F60, 05C70, 05E16

Toshiya Yurikusa  1

1 Nagoya University 
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     title = {Combinatorial cluster expansion formulas from triangulated surfaces},
     journal = {The electronic journal of combinatorics},
     year = {2019},
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     number = {2},
     doi = {10.37236/8351},
     zbl = {1436.13054},
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Toshiya Yurikusa. Combinatorial cluster expansion formulas from triangulated surfaces. The electronic journal of combinatorics, Tome 26 (2019) no. 2. doi: 10.37236/8351

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