Convex fair partitions into an arbitrary number of pieces

2018/04/09 by Akopyan, Arseniy, Avvakumov, Sergey, Karasev, Roman · 1 citation
#28A75 #52A38 #55R80 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1804.03057

Abstract

We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and perimeters for any integer m≥ 2; this result was previously known for prime powers m=p^k. We also discuss possible higher-dimensional generalizations and difficulties of extending our technique to equalizing more than one non-additive function.

Cited by

• Revisiting the Nandakumar-Ramana Rao Conjecture

Related

• Equipartition of several measures
• Fair partitions of the plane into incongruent pentagons
• A Set of Questions in Combinatorial and Metric Geometry
• Convex Regions and their 'Fairest' Equipartitioning Fans
• Convex Equipartitions via Equivariant Obstruction Theory