2023/11/16 by Soberón, Pablo, Yu, Christina
#28A75 #52A37 #55M20 #91B32 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2311.09905
A vast array of envy-free results have been found for the subdivision of one-dimensional resources, such as the interval [0,1]. The goal is to divide the space into n pieces and distribute them among n observers such that each receives their favorite pieces. We study high-dimensional versions of these results. We prove that several spaces of convex partitions of ℝd allow for envy-free division among any n observers. We also prove the existence of convex partitions of ℝd which allow for envy-free divisions among several groups of n observers simultaneously.