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math.AT2026
Avalanche homology of digraphs via sandpile dynamics
Henri Riihimäki, Jason P. Smith
We introduce avalanche homology as a new (di)graph homology theory, based on the dynamics of the sandpile model. Avalanche homology is the simplicial homology of the avalanche comp…
math.CO2026
Multipath complexes of bidirectional polygonal digraphs
Luigi Caputi, Carlo Collari, Jason P. Smith
In this work we study the homotopy type of multipath complexes of bidirectional path graphs and polygons, motivated by works of Vrećica and Živaljević on cycle-free chessboard comp…