Randomized trial shows representation stability in graph complexes, indicating implications for graph homology.
We prove a sharp representation stability result for graph complexes with a distinguished vertex, and prove that the chains realizing this sharp bound pass to non-trivial families of graph homology classes. This result may be interpreted as a higher genus generalization of Hersh and Reiner’s stability bound for configuration spaces of points in odd dimensional Euclidean space.
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Fedah et al. (2026) studied this question.
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