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math.CO2026
Area and water-capacity statistics for upper hulls of Dyck paths
Aleksander L. Owczarek, Thomas Prellberg
We study Dyck paths refined simultaneously by proper area and water capacity, where water capacity is measured above the path and below its lattice-path upper hull. The finite-heig…
cond-mat.stat-mech2026
Random sampling of self-avoiding theta-graphs
Nicholas R. Beaton, Aleksander L. Owczarek
Theta-graphs are a type of spatial graph with two vertices connected by three edges. We investigate embeddings of theta-graphs in the square and simple cubic lattices, using a comb…