Stasheff polytopes and the coordinate ring of the cluster \(\mathcal X\)-variety of type \(A_n\). (English) Zbl 1296.05210
Summary: We define Stasheff polytopes in the spaces of tropical points of cluster \(\mathcal A\)-varieties. We study the supports of products of elements of canonical bases for cluster \(\mathcal X\)-varieties. We prove that, for the cluster \(\mathcal X\)-variety of type \(A_n\), such supports are Stasheff polytopes.
MSC:
| 05E40 | Combinatorial aspects of commutative algebra |
| 13F60 | Cluster algebras |
| 14M99 | Special varieties |
| 14T99 | Tropical geometry |
| 52B99 | Polytopes and polyhedra |
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