Convex equipartitions via Equivariant Obstruction Theory
TLDR
In this paper, a regular cell complex model for the configuration space F(ℝ d, n) was described and the prime power case of the conjecture by Nandakumar and Ramana Rao that every polygon can be partitioned into n convex parts of equal area and perimeter.Abstract:
We describe a regular cell complex model for the configuration space F(ℝ
d
, n). Based on this, we use Equivariant Obstruction Theory to prove the prime power case of the conjecture by Nandakumar and Ramana Rao that every polygon can be partitioned into n convex parts of equal area and perimeter.read more
Citations
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Convex equipartitions: the spicy chicken theorem
TL;DR: In this article, it was shown that for any prime power and any convex body (i.e., a compact convex set with interior), there exists a partition of the body into convex sets with equal volumes and equal surface areas.
Journal ArticleDOI
Convex Equipartitions: The Spicy Chicken Theorem
TL;DR: In this paper, it was shown that for any prime power n and any convex body K, there exists a partition of K into n convex sets with equal volumes and equal surface areas.
Journal ArticleDOI
Fair and Square: Cake-cutting in Two Dimensions
TL;DR: The level of proportionality that can be guaranteed is examined, providing both impossibility results and constructive division procedures, particularly squares and fat rectangles.
Posted Content
Hyperplane mass partitions via relative equivariant obstruction theory
TL;DR: In this paper, a join scheme for the Grunbaum-Hadwiger-Ramos hyperplane mass partition problem was developed, such that non-existence of an $G_k$-equivariant map between spheres (S^d)^{*k} \rightarrow S(W_k\oplus U_k^{\oplus j})$ that extends a test map on the subspace of a sphere where the hyperoctahedral group $Gk$ acts non-freely, implies that $(d,j,k)$ is
Journal ArticleDOI
Equivariant topology of configuration spaces
TL;DR: In this article, the Fadell-Husseini index of the configuration space F (R, n) with respect to different subgroups of the symmetric group Sn was studied.
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Mark Goresky,Robert MacPherson +1 more
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