# Papers — Pablo Soberón Author-written context, when present, is attributed in each entry. It is not an independent assessment. # The topological Bárány–Larman conjecture for prime numbers Authors: Pablo Soberón Year: 2026 Status: preprint Paper page: https://www.psoberon.com/papers/barany-larman-primes/ arXiv: https://arxiv.org/abs/2609.37876 Topics: Tverberg theory; Topological combinatorics ## Abstract The Bárány–Larman conjecture states that for any d+1 sets of r points each in ℝᵈ, considered as color classes, we can partition their union into r rainbow (d+1)-tuples whose convex hulls intersect. We prove that the topological version of this conjecture holds when r is a prime number. We also show that the optimal colorful Tverberg theorem of Blagojević, Matschke, and Ziegler cannot be extended to prime powers. ## Overview The topological Bárány–Larman conjecture for prime numbers, and counterexamples to extending the optimal colorful Tverberg theorem to prime powers. --- # Discrepancy theory, Tverberg's theorem, and regression depth Authors: Aleksey Lopez; Pablo Soberón Year: 2026 Status: preprint Paper page: https://www.psoberon.com/papers/discrepancy-tverberg-regression/ arXiv: https://arxiv.org/abs/2609.24775 Topics: Tverberg theory; Discrepancy & tolerance Student coauthors: Aleksey Lopez ## Overview Discrepancy-theoretic bounds for Tverberg partitions with tolerance, for point sets and for regression hulls of hyperplanes. --- # Helly and Radon theorems for convex intersections containing k-flats Authors: Sarah Ludwigson; Pablo Soberón Year: 2026 Status: preprint Paper page: https://www.psoberon.com/papers/helly-radon-flats/ arXiv: https://arxiv.org/abs/2608.27189 Topics: Helly-type theorems; Tverberg theory; Topological combinatorics Student coauthors: Sarah Ludwigson ## Abstract We study versions of results in combinatorial geometry related to families of convex sets in ℝᵈ whose intersection contains a k-dimensional affine space. We prove generalizations of the colorful Radon theorem, the fractional Helly theorem, the colorful Helly theorem, and the selection-structure Helly theorem. When k=0, our arguments give new proofs of the corresponding versions for points. ## Overview Colorful and fractional intersection theorems for convex families whose intersection contains an affine k-flat. --- # Four hyperplanes do not always equipartition a mass in ℝ⁴ Authors: Pablo Soberón Year: 2026 Status: submitted Paper page: https://www.psoberon.com/papers/four-hyperplanes/ arXiv: https://arxiv.org/abs/2608.23312 Topics: Mass partitions ## Abstract We construct a smooth strictly positive density in ℝ⁴ that cannot be divided into 16 parts of the same size by four affine hyperplanes. This settles the last open case of Grünbaum's 1960 conjecture and disproves Ramos' general conjecture on hyperplane equipartitions. We reduce the construction to finding two homogeneous polynomials in four variables, of degrees three and four, whose multilinear coefficients cannot vanish simultaneously after any orthogonal change of coordinates. We give two proofs of this nonvanishing result. The first uses a local perturbation argument. The second reduces it to the absence of a common zero for five explicit polynomials on [−1,1]⁶, verified by a computer-assisted Bernstein subdivision argument. ## Overview A smooth positive density in four dimensions that admits no equipartition into sixteen equal parts by four affine hyperplanes. --- # Blocking codimension-one simplices on the moment curve Authors: Pablo Soberón Year: 2026 Status: submitted Paper page: https://www.psoberon.com/papers/moment-curve-blocking/ arXiv: https://arxiv.org/abs/2608.09829 Topics: Combinatorial convexity --- # Selection-structure generalizations of the Borsuk–Ulam theorem Authors: Pablo Soberón Year: 2026 Status: preprint Paper page: https://www.psoberon.com/papers/selection-borsuk-ulam/ arXiv: https://arxiv.org/abs/2607.21410 Topics: Topological combinatorics; Tverberg theory --- # KKM theorems and discrete geometry beyond matroids Authors: Pablo Soberón Year: 2026 Status: submitted Paper page: https://www.psoberon.com/papers/beyond-matroids/ arXiv: https://arxiv.org/abs/2606.16832 Topics: Topological combinatorics; Helly-type theorems; Tverberg theory ## Overview Selection structures extend the role of color classes and matroids in KKM theorems and discrete geometry. --- # Variations of Helly's theorem for convex splinters Authors: Pablo Soberón; Iris Ye Year: 2026 Status: preprint Paper page: https://www.psoberon.com/papers/convex-splinters/ arXiv: https://arxiv.org/abs/2606.23437 Topics: Helly-type theorems; Tverberg theory; Combinatorial convexity Student coauthors: Iris Ye --- # Tverberg cores and Kalai’s cascade conjecture Authors: Pablo Soberón Year: 2026 Status: submitted Paper page: https://www.psoberon.com/papers/tverberg-cores/ arXiv: https://arxiv.org/abs/2605.21305 Topics: Tverberg theory; Topological combinatorics ## Abstract We study topological analogues of Kalai's cascade conjecture. Given a continuous map from an n-simplex to ℝᵈ, let Tᵣ(f) be the set of points contained in the images of r pairwise disjoint faces. We prove that if r is a prime power and dim Tᵣ(f) ≤ k, then there exists a point that remains an r-Tverberg point after any t vertices are deleted, provided n = (r−1)(d+1) + t(k+1). For t=1, this gives a topological analogue of a standard consequence of Kalai's cascade conjecture. We also confirm the cascade conjecture for finite point sets whose Radon set is 0-dimensional. ## Overview Topological Tverberg cores, vertex-deletion tolerance, and consequences for Kalai’s cascade conjecture. --- # An elementary proof of Sierksma's conjecture for seven points in the plane Authors: Pablo Soberón Year: 2026 Status: submitted Paper page: https://www.psoberon.com/papers/sierksma-seven-points/ arXiv: https://arxiv.org/abs/2604.18485 Topics: Tverberg theory --- # High-dimensional envy-free partitions Authors: Christina Yu; Pablo Soberón Year: 2026 Status: published Paper page: https://www.psoberon.com/papers/high-dimensional-envy-free/ Reference: Comb. Theory 6, no. 1, Paper No. 11, 19 pp. arXiv: https://arxiv.org/abs/2311.09905 Topics: Fair division; Topological combinatorics Student coauthors: Christina Yu --- # Fair distribution of bundles Authors: Pablo Soberón Year: 2026 Status: published Paper page: https://www.psoberon.com/papers/fair-distribution-bundles/ Reference: Proc. Amer. Math. Soc. 154, no. 7, 3085–3097. arXiv: https://arxiv.org/abs/2507.13421 Topics: Fair division; Topological combinatorics --- # Partitions of mass assignments with spheres and wedges Authors: Deron Lessure; Pablo Soberón Year: 2025 Status: accepted Paper page: https://www.psoberon.com/papers/mass-assignments-spheres-wedges/ Reference: Accepted in European Journal of Combinatorics arXiv: https://arxiv.org/abs/2507.06919 Topics: Mass partitions Student coauthors: Deron Lessure --- # Colorful and Quantitative Variations of Krasnosselsky's Theorem Authors: Connor Donovan; Danielle Paulson; Pablo Soberón Year: 2025 Status: published Paper page: https://www.psoberon.com/papers/krasnosselsky-colorful-quantitative/ Reference: Studia Sci. Math. Hungar. 62 (2025), no. 4, 336–353. arXiv: https://arxiv.org/abs/2304.04828 Topics: Helly-type theorems; Combinatorial convexity Student coauthors: Connor Donovan; Danielle Paulson --- # Tverberg Partition Graphs Authors: Deborah Oliveros; Érika Roldán; Pablo Soberón; Antonio J. Torres Year: 2025 Status: published Paper page: https://www.psoberon.com/papers/tverberg-partition-graphs/ Reference: SIAM J. Discrete Math. 39 (2), 863–880. arXiv: https://arxiv.org/abs/2310.08563 Topics: Tverberg theory; Graph theory --- # Extensions of discrete Helly theorems for boxes Authors: Timothy Edwards; Pablo Soberón Year: 2025 Status: published Paper page: https://www.psoberon.com/papers/discrete-helly-boxes/ Reference: SIAM J. Discrete Math. 39 (2), 1349–1362. arXiv: https://arxiv.org/abs/2404.14308 Topics: Helly-type theorems; Combinatorial convexity Student coauthors: Timothy Edwards --- # Tverberg's theorem and multi-class support vector machines Authors: Pablo Soberón Year: 2025 Status: published Paper page: https://www.psoberon.com/papers/tverberg-support-vector-machines/ Reference: Found. Data Sci. 7 (2), 568–580. arXiv: https://arxiv.org/abs/2404.16724 DOI: https://doi.org/10.3934/fods.2024039 Topics: Tverberg theory --- # Cookie cutters: Bisections with fixed shapes Authors: Patrick Schnider; Pablo Soberón Year: 2025 Status: published Paper page: https://www.psoberon.com/papers/cookie-cutters/ Reference: Adv. in Appl. Math. 171, Paper No. 102957, 15 pp. arXiv: https://arxiv.org/abs/2502.17176 Topics: Mass partitions --- # Generalizations of the Yao–Yao partition theorem and the central transversal theorem Authors: Michael N. Manta; Pablo Soberón Year: 2024 Status: published Paper page: https://www.psoberon.com/papers/yao-yao-central-transversals/ Reference: Discrete Comput. Geom. 71 (4), 1381–1402. arXiv: https://arxiv.org/abs/2107.06233 Topics: Mass partitions Student coauthors: Michael N. Manta --- # Bisections of mass assignments using flags of affine spaces Authors: Ilani Axelrod-Freed; Pablo Soberón Year: 2024 Status: published Paper page: https://www.psoberon.com/papers/mass-assignments-flags/ Reference: Discrete Comput. Geom. 72 (2), 550–568. arXiv: https://arxiv.org/abs/2109.13106 Topics: Mass partitions; Topological combinatorics Student coauthors: Ilani Axelrod-Freed --- # Improved Tverberg theorems for certain families of polytopes Authors: Pablo Soberón; Shira Zerbib Year: 2024 Status: accepted Paper page: https://www.psoberon.com/papers/tverberg-polytopes/ Reference: Accepted to Discrete Comput. Geom. arXiv: https://arxiv.org/abs/2404.11533 Topics: Tverberg theory --- # Bisections of mass assignments by parallel hyperplanes Authors: Nikola Sadovek; Pablo Soberón Year: 2024 Status: submitted Paper page: https://www.psoberon.com/papers/mass-assignments-parallel/ arXiv: https://arxiv.org/abs/2412.04058 Topics: Mass partitions; Topological combinatorics --- # Complex analogues of the Tverberg–Vrećica conjecture and central transversal theorems Authors: Nikola Sadovek; Pablo Soberón Year: 2024 Status: published Paper page: https://www.psoberon.com/papers/complex-tverberg-vrecica/ Reference: Trans. Amer. Math. Soc. 379 (2026), no. 5, 3665–3691. arXiv: https://arxiv.org/abs/2408.14337 Topics: Mass partitions; Tverberg theory; Topological combinatorics --- # Bisecting masses with families of parallel hyperplanes Authors: Alfredo Hubard; Pablo Soberón Year: 2024 Status: submitted Paper page: https://www.psoberon.com/papers/bisecting-parallel-families/ arXiv: https://arxiv.org/abs/2404.14320 Topics: Mass partitions --- # Combinatorial Depth Measures for Hyperplane Arrangements Authors: Patrick Schnider; Pablo Soberón Year: 2023 Status: published Paper page: https://www.psoberon.com/papers/hyperplane-depth/ Reference: 39th International Symposium on Computational Geometry, Art. No. 55, 14 pp., LIPIcs 258. arXiv: https://arxiv.org/abs/2302.07768 DOI: https://doi.org/10.4230/LIPIcs.SoCG.2023.55 Topics: Tverberg theory; Combinatorial convexity --- # Lifting methods in mass partition problems Authors: Pablo Soberón; Yuki Takahashi Year: 2023 Status: published Paper page: https://www.psoberon.com/papers/lifting-mass-partitions/ Reference: Int. Math. Res. Not. IMRN 2023 (16), 14103–14130. arXiv: https://arxiv.org/abs/2109.03749 DOI: https://doi.org/10.1093/imrn/rnac224 Topics: Mass partitions; Topological combinatorics Student coauthors: Yuki Takahashi --- # Fair distributions for more participants than allocations Authors: Pablo Soberón Year: 2022 Status: published Paper page: https://www.psoberon.com/papers/more-participants-than-allocations/ Reference: Proc. Amer. Math. Soc., Ser. B 9, 404–414. arXiv: https://arxiv.org/abs/2110.03600 Topics: Fair division; Topological combinatorics --- # Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes Authors: João Pedro Carvalho; Pablo Soberón Year: 2022 Status: published Paper page: https://www.psoberon.com/papers/colorful-hyperplane-counterexamples/ Reference: Acta Mathematica Hungarica 167, 385–392. arXiv: https://arxiv.org/abs/2108.07680 Topics: Tverberg theory Student coauthors: João Pedro Carvalho --- # A survey of mass partitions Authors: Edgardo Roldán-Pensado; Pablo Soberón Year: 2022 Status: published Paper page: https://www.psoberon.com/papers/mass-partitions-survey/ Reference: Bull. Amer. Math. Soc. 59 (2), 227–267. arXiv: https://arxiv.org/abs/2010.00478 Topics: Mass partitions --- # Tolerance for colorful Tverberg partitions Authors: Sherry Sarkar; Pablo Soberón Year: 2022 Status: published Paper page: https://www.psoberon.com/papers/colorful-tverberg-tolerance/ Reference: European J. Combin. 103, Paper No. 103527. arXiv: https://arxiv.org/abs/2005.13495 Topics: Tverberg theory Student coauthors: Sherry Sarkar --- # Isometric and affine copies of a set in volumetric Helly results Authors: John A. Messina; Pablo Soberón Year: 2022 Status: published Paper page: https://www.psoberon.com/papers/volumetric-helly-copies/ Reference: Comput. Geom. 103, Paper No. 101855. arXiv: https://arxiv.org/abs/2010.04135 Topics: Helly-type theorems; Combinatorial convexity Student coauthors: John A. Messina --- # Quantitative combinatorial geometry for concave functions Authors: Sherry Sarkar; Alexander Xue; Pablo Soberón Year: 2021 Status: published Paper page: https://www.psoberon.com/papers/concave-functions/ Reference: J. Combin. Theory Ser. A 182, Article 105465. arXiv: https://arxiv.org/abs/1908.04438 Topics: Helly-type theorems; Tverberg theory; Combinatorial convexity Student coauthors: Sherry Sarkar; Alexander Xue --- # Balanced convex partitions of lines in the plane Authors: Alexander Xue; Pablo Soberón Year: 2021 Status: published Paper page: https://www.psoberon.com/papers/balanced-partitions-lines/ Reference: Discrete Comput. Geom. 66 (3), 1150–1167. arXiv: https://arxiv.org/abs/1910.06231 Topics: Mass partitions Student coauthors: Alexander Xue --- # Tverberg's theorem, disks, and Hamiltonian cycles Authors: Pablo Soberón; Yaqian Tang Year: 2021 Status: published Paper page: https://www.psoberon.com/papers/tverberg-disks-hamiltonian/ Reference: Ann. Comb. 25, 995–1005. arXiv: https://arxiv.org/abs/2011.12218 Topics: Tverberg theory; Graph theory Student coauthors: Yaqian Tang --- # Finite groups as prescribed polytopal symmetries Authors: Alexandru Chirvasitu; Frieder Ladisch; Pablo Soberón Year: 2021 Status: published Paper page: https://www.psoberon.com/papers/finite-groups-polytopes/ Reference: Israel J. Math. 245 (1), 75–91. arXiv: https://arxiv.org/abs/1907.10022 Topics: Polytopes & symmetry; Combinatorial convexity --- # A mélange of diameter Helly-type theorems Authors: Travis Dillon; Pablo Soberón Year: 2021 Status: published Paper page: https://www.psoberon.com/papers/diameter-helly-melange/ Reference: SIAM J. Discrete Math. 35 (3), 1615–1627. arXiv: https://arxiv.org/abs/2008.13737 Topics: Helly-type theorems; Combinatorial convexity Student coauthors: Travis Dillon --- # Prescribing Symmetries and Automorphisms for Polytopes Authors: Egon Schulte; Pablo Soberón; Gordon Ian Williams Year: 2021 Status: published Paper page: https://www.psoberon.com/papers/prescribing-polytope-symmetries/ Reference: Polytopes and Discrete Geometry, Contemporary Mathematics 764, American Mathematical Society, 221–233. arXiv: https://arxiv.org/abs/1902.05439 Topics: Polytopes & symmetry; Combinatorial convexity --- # The topological Tverberg problem beyond prime powers Authors: Florian Frick; Pablo Soberón Year: 2020 Status: preprint Paper page: https://www.psoberon.com/papers/topological-tverberg-beyond-prime-powers/ arXiv: https://arxiv.org/abs/2005.05251 Topics: Tverberg theory; Topological combinatorics ## Author correction notice The authors’ arXiv v2 comments report a gap in the proof of Theorem 1.1. The revised manuscript explains the gap; the original main theorem is not presented here as established. Source: https://arxiv.org/abs/2005.05251v2 --- # A Note on the Maximum Rectilinear Crossing Number of Spiders Authors: Joshua Fallon; Kirsten Hogenson; Lauren Keough; Mario Lomelí; Marcus Schaefer; Pablo Soberón Year: 2020 Status: published Paper page: https://www.psoberon.com/papers/rectilinear-crossings-spiders/ Reference: J. Combin. Math. Combin. Comput. 113, 127–139. arXiv: https://arxiv.org/abs/1808.00385 Topics: Graph theory --- # Tverberg partitions as weak epsilon-nets Authors: Pablo Soberón Year: 2019 Status: published Paper page: https://www.psoberon.com/papers/tverberg-weak-nets/ Reference: Combinatorica 39 (2), 447–458. arXiv: https://arxiv.org/abs/1711.11496 Topics: Tverberg theory --- # Cutting a part of many measures Authors: Pavle V. M. Blagojević; Nevena Palić; Pablo Soberón; Günter M. Ziegler Year: 2019 Status: published Paper page: https://www.psoberon.com/papers/cutting-many-measures/ Reference: Forum of Mathematics, Sigma 7, E37. arXiv: https://arxiv.org/abs/1710.05118 Topics: Mass partitions --- # Robust Tverberg and colorful Carathéodory results via random choice Authors: Pablo Soberón Year: 2018 Status: published Paper page: https://www.psoberon.com/papers/robust-random-choice/ Reference: Combinatorics, Probability and Computing 27 (3), 427–440. arXiv: https://arxiv.org/abs/1606.08790 Topics: Tverberg theory; Discrepancy & tolerance --- # Tverberg’s theorem is 50 years old: a survey Authors: Imre Bárány; Pablo Soberón Year: 2018 Status: published Paper page: https://www.psoberon.com/papers/tverberg-fifty-years/ Reference: Bull. Amer. Math. Soc. 55 (4), 459–492. arXiv: https://arxiv.org/abs/1712.06119 Topics: Tverberg theory --- # Tverberg plus minus Authors: Imre Bárány; Pablo Soberón Year: 2018 Status: published Paper page: https://www.psoberon.com/papers/tverberg-plus-minus/ Reference: Discrete Comput. Geom. 60 (3), 588–598. arXiv: https://arxiv.org/abs/1612.05630 Topics: Tverberg theory --- # Thieves can make sandwiches Authors: Pavle V. M. Blagojević; Pablo Soberón Year: 2018 Status: published Paper page: https://www.psoberon.com/papers/thieves-sandwiches/ Reference: Bull. London Math. Soc. 50 (1), 108–123. arXiv: https://arxiv.org/abs/1706.03640 Topics: Mass partitions; Topological combinatorics --- # Computing the Partition Function for Graph Homomorphisms Authors: Alexander Barvinok; Pablo Soberón Year: 2017 Status: published Paper page: https://www.psoberon.com/papers/graph-homomorphism-partition-function/ Reference: Combinatorica 37 (4), 633–650. arXiv: https://arxiv.org/abs/1410.1842 Topics: Graph theory --- # Quantitative (p, q) theorems in combinatorial geometry Authors: David Rolnick; Pablo Soberón Year: 2017 Status: published Paper page: https://www.psoberon.com/papers/quantitative-pq/ Reference: Discrete Math. 340 (10), 2516–2527. arXiv: https://arxiv.org/abs/1504.01642 Topics: Helly-type theorems; Combinatorial convexity --- # Quantitative Tverberg theorems over lattices and other discrete sets Authors: Jesús A. De Loera; Reuben N. La Haye; David Rolnick; Pablo Soberón Year: 2017 Status: published Paper page: https://www.psoberon.com/papers/quantitative-tverberg-lattices/ Reference: Discrete Comput. Geom. 58 (2), 435–458. arXiv: https://arxiv.org/abs/1603.05525 Topics: Tverberg theory; Helly-type theorems; Combinatorial convexity --- # Tensors, colors, and convex hulls Authors: Pablo Soberón Year: 2017 Status: published Paper page: https://www.psoberon.com/papers/tensors-colors-convex-hulls/ Reference: Discrete Geometry and Convexity: in honour of Imre Bárány, edited by Gergely Ambrus, Károly J. Böröczky and Zoltán Füredi, 97–101. ISBN 978 963 279 963 6. Topics: Tverberg theory --- # Helly’s Theorem: New Variations and Applications Authors: Nina Amenta; Jesús A. De Loera; Pablo Soberón Year: 2017 Status: published Paper page: https://www.psoberon.com/papers/helly-new-variations-survey/ Reference: Algebraic and Geometric Methods in Discrete Mathematics, Contemporary Mathematics 685, American Mathematical Society, 55–95. arXiv: https://arxiv.org/abs/1508.07606 Topics: Helly-type theorems; Combinatorial convexity --- # Quantitative combinatorial geometry for continuous parameters Authors: Jesús A. De Loera; Reuben N. La Haye; David Rolnick; Pablo Soberón Year: 2017 Status: published Paper page: https://www.psoberon.com/papers/quantitative-continuous-parameters/ Reference: Discrete Comput. Geom. 57 (2), 318–334. arXiv: https://arxiv.org/abs/1603.05523 Topics: Helly-type theorems; Tverberg theory; Combinatorial convexity --- # Positive-fraction intersection results and variations of weak epsilon-nets Authors: Alexander Magazinov; Pablo Soberón Year: 2017 Status: published Paper page: https://www.psoberon.com/papers/positive-fraction-weak-nets/ Reference: Monatshefte für Mathematik 183 (1), 165–176. arXiv: https://arxiv.org/abs/1506.02191 Topics: Helly-type theorems; Combinatorial convexity --- # Algorithms for Tverberg's theorem via centerpoint theorems Authors: David Rolnick; Pablo Soberón Year: 2016 Status: preprint Paper page: https://www.psoberon.com/papers/algorithms-tverberg-centerpoints/ arXiv: https://arxiv.org/abs/1601.03083 Topics: Tverberg theory --- # Helly-type theorems for the diameter Authors: Pablo Soberón Year: 2016 Status: published Paper page: https://www.psoberon.com/papers/helly-diameter/ Reference: Bull. London Math. Soc. 48 (4), 577–588. arXiv: https://arxiv.org/abs/1509.07908 Topics: Helly-type theorems; Tverberg theory; Combinatorial convexity --- # Computing the Partition Function for Graph Homomorphisms with Multiplicities Authors: Alexander Barvinok; Pablo Soberón Year: 2016 Status: published Paper page: https://www.psoberon.com/papers/graph-homomorphisms-multiplicities/ Reference: J. Combin. Theory Ser. A 137, 1–26. arXiv: https://arxiv.org/abs/1406.1771 Topics: Graph theory --- # Measure Partitions Using Hyperplanes with Fixed Directions Authors: Roman N. Karasev; Edgardo Roldán-Pensado; Pablo Soberón Year: 2016 Status: published Paper page: https://www.psoberon.com/papers/fixed-direction-hyperplanes/ Reference: Israel J. Math. 212 (2), 705–708. arXiv: https://arxiv.org/abs/1408.4830 Topics: Mass partitions --- # About an Erdős–Grünbaum conjecture concerning piercing of non bounded convex sets Authors: Amanda Montejano; Luis Montejano; Edgardo Roldán-Pensado; Pablo Soberón Year: 2015 Status: published Paper page: https://www.psoberon.com/papers/erdos-grunbaum-piercing/ Reference: Discrete Comput. Geom. 53 (4), 941–950. arXiv: https://arxiv.org/abs/1407.0642 Topics: Helly-type theorems; Combinatorial convexity --- # On a Problem by Dol’nikov Authors: Jesús Jerónimo-Castro; Alexander Magazinov; Pablo Soberón Year: 2015 Status: published Paper page: https://www.psoberon.com/papers/dolnikov-problem/ Reference: Discrete Math. 338 (9), 1577–1585. arXiv: https://arxiv.org/abs/1310.4714 Topics: Helly-type theorems; Combinatorial convexity --- # Equal coefficients and tolerance in coloured Tverberg partitions Authors: Pablo Soberón Year: 2015 Status: published Paper page: https://www.psoberon.com/papers/equal-coefficients/ Reference: Combinatorica 35 (2), 235–252. arXiv: https://arxiv.org/abs/1204.1202 Topics: Tverberg theory --- # An Extension of a Theorem by Yao & Yao Authors: Edgardo Roldán-Pensado; Pablo Soberón Year: 2014 Status: published Paper page: https://www.psoberon.com/papers/yao-yao-extension/ Reference: Discrete Comput. Geom. 51 (2), 285–289. arXiv: https://arxiv.org/abs/1112.5737 Topics: Mass partitions --- # Balanced Convex Partitions of Measures in ℝᵈ Authors: Pablo Soberón Year: 2012 Status: published Paper page: https://www.psoberon.com/papers/balanced-convex-measures/ Reference: Mathematika 58, 71–76. arXiv: https://arxiv.org/abs/1010.6191 DOI: https://doi.org/10.1112/S0025579311001914 Topics: Mass partitions; Topological combinatorics --- # A Generalisation of Tverberg’s Theorem Authors: Pablo Soberón; Ricardo Strausz Year: 2012 Status: published Paper page: https://www.psoberon.com/papers/generalisation-tverberg/ Reference: Discrete Comput. Geom. 47 (3), 455–460. DOI: https://doi.org/10.1007/s00454-011-9379-z Topics: Tverberg theory --- # Piercing Numbers for Balanced and Unbalanced Families Authors: Luis Montejano; Pablo Soberón Year: 2011 Status: published Paper page: https://www.psoberon.com/papers/piercing-balanced-families/ Reference: Discrete Comput. Geom. 45 (2), 358–364. DOI: https://doi.org/10.1007/s00454-010-9295-7 Topics: Helly-type theorems; Combinatorial convexity