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Tverberg-type theory aims to establish sufficient conditions for a simplicial complex $\Sigma$ such that every continuous map $f\colon \Sigma \to \mathbb{R}^d$ maps $q$ points from pairwise disjoint faces to the same point in $\mathbb{R}^d$.
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Albrecht Dold, Simple proofs of some Borsuk–Ulam results , Contemp. Math. 19
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Imre Bárány and David G. Larman, A Colored Version of Tverberg’s Theorem , J. Lond. Math. Soc s2-45
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Rade T. Živaljević and Siniša T. Vrećica, The colored Tverberg’s problem and complexes of injective functions , J. Combin. Theory, Ser. A 61
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Aleksei Yu. Volovikov, On a topological generalization of the Tverberg theorem , Math. Notes 59
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Dmitry N. Kozlov, Complexes of Directed Trees , J. Combin. Theory, Ser. A 88
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Jiří Matoušek, Using the Borsuk–Ulam theorem: Lectures on Topological Methods in Combinatorics and Geometry , Springer Science & Business Media, 2003
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Torsten Schöneborn and Günter M. Ziegler, The topological Tverberg theorem and winding numbers , J. Combin. Theory, Ser. A 112
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Pavle V. M. Blagojević, Benjamin Matschke, and Günter M. Ziegler, Optimal bounds for a colorful Tverberg-Vrecica type problem , Adv. Math. 226
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2015
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Pablo Soberón, Equal coefficients and tolerance in coloured Tverberg partitions , Combinatorica 35
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Imre Bárány, Pavle V. M. Blagojević, and Günter M. Ziegler, Tverberg’s theorem at 50: extensions and counterexamples , Notices Amer. Math. Soc. 63
2016
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Pavle V. M. Blagojević and Günter M. Ziegler, Beyond the Borsuk–Ulam Theorem: The Topological Tverberg Story , A Journey Through Discrete Mathematics: A Tribute to Jiří Matoušek (Martin Loebl, Jaroslav Nešetřil, and Robin Thomas, eds.), Springer International Publishing, Cham, 2017, pp. 273–341
2017
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Pavle V. M. Blagojević, Florian Frick, and Günter M. Ziegler, Tverberg plus constraints , Bull. Lond. Math. Soc. 46
2014
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Isaac Mabillard and Uli Wagner, Eliminating Tverberg points, I. An analogue of the Whitney trick , Proc. 30th Annual Symp. Comput. Geom. (SOCG) (Kyoto), ACM, 2014, pp. 171–180
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Pavle V. M. Blagojević, Benjamin Matschke, and Günter M. Ziegler, Optimal bounds for the colored Tverberg problem , J. Europ. Math. Soc. (JEMS) 17
2015
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Florian Frick, Counterexamples to the topological Tverberg conjecture , Oberwolfach Rep. 12
2015
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Peter Gustav Lejeune Dirichlet, Beweis des Satzes, dass jede unbegrenzte arithmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Factor sind, unendlich viele Primzahlen enthält , Abh. K. Preuss. Akad. Wiss. 45
Cited in the paper.
Murad Özaydin, Equivariant maps for the symmetric group , available at https://minds.wisconsin.edu/bitstream/handle/1793/63829/Ozaydin.pdf
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Imre Bárány and Pablo Soberón, Tverberg’s theorem is 50 years old: a survey , Bull. Amer. Math. Soc. 55
2018
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2019
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Pavle V. M. Blagojević, Florian Frick, and Günter M. Ziegler, Barycenters of polytope skeleta and counterexamples to the topological Tverberg conjecture, via constraints , J. Europ. Math. Soc. (JEMS) 21
2019
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Jesús De Loera, Xavier Goaoc, Frédéric Meunier, and Nabil Mustafa, The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg , Bull. Amer. Math. Soc. 56
2019
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