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math.CO2026
Cluster tori over , hexagonal moves on triangulations, and minimal coverings of cluster manifolds
Daniel Pérez Melesio, José Simental
We study cluster algebras over . By the Laurent phenomenon there is a map from the set of seeds of the cluster algebra to the corresponding cluster variety. We show t…
math.CO2026
Mysterious points in keys but not trees
Scott Neville, José Simental
The deep locus of a cluster variety is defined to be the set of its points that do not belong to any cluster torus. We show that, if the cluster variety has a seed whose mutable pa…
math.CO2026
Bruhat intervals that are large hypercubes
Jordan Ellenberg, Nicolas Libedinsky, David Plaza +2
We study the question of finding big Bruhat intervals that are poset hypercubes in the symmetric group . Using permutations suggested by AlphaEvolve (an evolutionary coding ag…