Mass partitions

Research

MEASURE PARTITIONS

Bisecting masses with families of parallel hyperplanes

Joint with Alfredo Hubard

Year:

2024

Status

arXiv version

Extensions of discrete Helly theorems for boxes

Joint with Timothy Edwards

Year:

2024

Status:

arXiv version

High-dimensional envy-free partitions

Joint with Christina Yu

Year:

2023

Status:

Submitted for Publication

arXiv version

Lifting methods in mass partition problems

Joint with Yuki Takahashi

Year:

2023

Reference:

Int. Math. Res. Not. IMRN, 2023 (16), pp. 14103-14130

arXiv version

Combinatorial Depth Measures for Hyperplane Arrangements

Joint with Patrick Schnider

Year:

2023

Status:

Accepted to SoCG 2023

arXiv version

Fair distributions for more participants than allocations

Year:

2022

Reference:

Proc. Amer. Math. Soc., Ser. B 9 pp. 404–414

arXiv version

A survey of mass partitions

Joint with Edgardo Roldán-Pensado

Year:

2022

Reference:

Bull. Amer. Math. Soc. 59(2) pp. 227-267

arXiv version

Generalizations of the Yao-Yao partition theorem and the central transversal theorem

Joint with Michael N. Manta

Year:

2021

Status:

Submitted to journal

arXiv version

Balanced convex partitions of lines in the plane

Joint with Alexander Xue

Year:

2021

Reference:

Discrete Comput. Geom. 66(3), pp 1150-1167

arXiv version

Bisections of mass assignments using flags of affine spaces

Joint with Ilani Axelrod-Freed

Year:

2021

Status:

Accepted at Discrete Comput. Geom.

arXiv version

Cutting a part of many measures

Joint with Pavle V. M. Blagojevic, Nevena Palic, and Günter M. Ziegler

Year:

2019

Reference:

Forum of Mathematics, Sigma 7 E37

arXiv version

Thieves can make sandwiches

Joint with Pavle V. M. Blagojevic

Year:

2018

Reference:

Bull. London Math. Soc. 50 (1) pp.108–123

arXiv version

Measure Partitions Using Hyperplanes with Fixed
Directions

Joint with Roman Karasev and Edgardo Roldán-Pensado

Year:

2016

Reference:

Israel J. Math. 212(2) pp 705–708

arXiv version

An Extension of a Theorem by Yao & Yao

Joint with Edgardo Roldán-Pensado

Year:

2014

Reference:

Discrete Comput. Geom.
51(2), pp.285-289

arXiv version

Balanced Convex Partitions of Measures in R^d

Year:

2012

Reference:

Mathematika 58, pp.71-76

arXiv version

MEASURE PARTITIONS

Bisecting masses with families of parallel hyperplanes

Extensions of discrete Helly theorems for boxes

High-dimensional envy-free partitions

Lifting methods in mass partition problems

Combinatorial Depth Measures for Hyperplane Arrangements

Fair distributions for more participants than allocations

A survey of mass partitions

Generalizations of the Yao-Yao partition theorem and the central transversal theorem

Balanced convex partitions of lines in the plane

Bisections of mass assignments using flags of affine spaces

Cutting a part of many measures

Thieves can make sandwiches

Measure Partitions Using Hyperplanes with FixedDirections

An Extension of a Theorem by Yao & Yao

Balanced Convex Partitions of Measures in R^d

Measure Partitions Using Hyperplanes with Fixed
Directions