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A decade ago two groups of authors, Karasev, Hubard and Aronov, and Blagojevi\'c and Ziegler, have shown that the regular convex partitions of a Euclidean space into $n$ parts yield a solution to the generalised Nandakumar and Ramana-Rao conjecture when $n$ is a prime power.
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R. Nandakumar, “Fair” partitions , Blog entry, September 28, 2006, http://nandacumar.blogspot.de/2006/09/cutting-shapes.html
2006
Cited alongside, same era.
Pavle V. M. Blagojević and Aleksandra S. Dimitrijević Blagojević, Using equivariant obstruction theory in combinatorial geometry , Topology Appl. 154
2007
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Imre Bárány, Pavle Blagojević, and András Szűcs, Equipartitioning by a convex 3-fan , Adv. Math. 223
2010
Cited alongside, same era.
2011
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2014
Later among the works it cites.
Pavle V. M. Blagojević, Wolfgang Lück, and Günter M. Ziegler, Equivariant topology of configuration spaces , J. Topol. 8
2015
Later among the works it cites.
Hans Wilhelm Alt, Linear functional analysis , Universitext, Springer-Verlag London, Ltd., London, 2016, An application-oriented introduction, Translated from the German edition by Robert Nürnberg
2016
Later among the works it cites.
Arseniy Akopyan, Sergey Avvakumov, and Roman Karasev, Convex fair partitions into an arbitrary number of pieces , Arxiv preprint (2018), 1804.03057
2018
Later among the works it cites.
Pavle V. M. Blagojević and Pablo Soberón, Thieves can make sandwiches , Bull. Lond. Math. Soc. 50
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2011
Cited alongside, same era.
Yashar Memarian, On Gromov’s waist of the sphere theorem , J. Topol. Anal. 3
2011
Cited alongside, same era.
R. Nandakumar and N. Ramana Rao, Fair partitions of polygons: an elementary introduction , Proc. Indian Acad. Sci. Math. Sci. 122
2012
Cited alongside, same era.
Pablo Soberón, Balanced convex partitions of measures in ℝ d \mathbb{R}^{d} , Mathematika 58
2012
Cited alongside, same era.
Darius Geiß, Rolf Klein, Rainer Penninger, and Günter Rote, Optimally solving a transportation problem using Voronoi diagrams , Comput. Geom. 46
2013
Cited alongside, same era.
Pavle V. M. Blagojević and Günter M. Ziegler, Convex equipartitions via equivariant obstruction theory , Israel J. Math. 200
2014
Cited alongside, same era.
2018
Later among the works it cites.
Nevena Palić, Grassmannians, measure partitions, and waists of spheres , PhD thesis, Freie Universität Berlin, 2018
2018
Later among the works it cites.
Sergey Avvakumov and Sergey Kudrya, Vanishing of all equivariant obstructions and the mapping degree , Discrete and Computational Geometry 66
2021
Later among the works it cites.
Pavle V. M. Blagojević, Frederick R. Cohen, Michael C. Crabb, Wolfgang Lück, and Günter M. Ziegler, Equivariant cohomology of configuration spaces mod 2 {\rm mod}\,2 —the state of the art , Lecture Notes in Mathematics, vol. 2282, Springer, Cham, [2021] ©2021
2021
Later among the works it cites.
Sergey Avvakumov, Roman Karasev, and Arkadiy Skopenkov, Stronger counterexamples to the topological tverberg conjecture , Combinatorica 43
2023
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