Mass partitions

Research

MEASURE PARTITIONS

High-dimensional envy-free partitions

Joint with Christina Yu

Year:

2026

Reference:

Comb. Theory 6, no. 1, Paper No. 11, 19 pp.

arXiv version

Partitions of mass assignments with spheres and wedges

Joint with Deron Lessure

Year:

2025

Status:

Submitted for publication

arXiv version

Extensions of discrete Helly theorems for boxes

Joint with Timothy Edwards

Year:

2025

Reference:

SIAM J. Discrete Math. 39 (2), 1349-1362

arXiv version

Cookie cutters: Bisections with fixed shapes

Joint with Patrick Schnider

Year:

2025

Reference:

Adv. in Appl. Math. 171, Paper No. 102957, 15 pp.

arXiv version

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

Joint with Michael N. Manta

Year:

2024

Reference:

Discrete Comput. Geom. 71 (4), 1381-1402

arXiv version

Bisections of mass assignments using flags of affine spaces

Joint with Ilani Axelrod-Freed

Year:

2024

Reference:

Discrete Comput. Geom. 72 (2), 550-568

arXiv version

Bisections of mass assignments by parallel hyperplanes

Joint with Nikola Sadovek

Year:

2024

Status:

Submitted for publication

arXiv version

Bisecting masses with families of parallel hyperplanes

Joint with Alfredo Hubard

Year:

2024

Status

Submitted for publication

arXiv version

Combinatorial Depth Measures for Hyperplane Arrangements

Joint with Patrick Schnider

Year:

2023

Reference

39th International Symposium on Computational Geometry, Art. No. 55, 14 pp., LIPIcs. Leibniz Int. Proc. Inform., 258, Schloss Dagstuhl. Leibniz-Zent.

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

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

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

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

High-dimensional envy-free partitions

Partitions of mass assignments with spheres and wedges

Extensions of discrete Helly theorems for boxes

Cookie cutters: Bisections with fixed shapes

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

Bisections of mass assignments using flags of affine spaces

Bisections of mass assignments by parallel hyperplanes

Bisecting masses with families of parallel hyperplanes

Combinatorial Depth Measures for Hyperplane Arrangements

Lifting methods in mass partition problems

Fair distributions for more participants than allocations

A survey of mass partitions

Balanced convex partitions of lines in the plane

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