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math.CO2024
Bisecting masses with families of parallel hyperplanes
Alfredo Hubard, Pablo Soberón
We prove a common generalization of several mass partition results using hyperplane arrangements to split into two sets. Our main result implies the ham sandwich the…
math.CO2024
Crossing lemmas for -systems of arcs
Alfredo Hubard, Hugo Parlier
We show a generalization of the crossing lemma for multi-graphs drawn on orientable surfaces in which pairs of edges are assumed to be drawn by non-homotopic simple arcs which pair…