Fetching the paper…
Reading the bibliography…
Motivated by general probability theory, we say that the set $S$ in $\mathbb{R}^d$ is \emph{antipodal of rank $k$}, if for any $k+1$ elements $q_1,\ldots q_{k+1}\in S$, there is an affine map from $\mathrm{conv}(S)$ to the $k$-dimensional simplex $\Delta_k$ that maps $q_1,\ldots q_{k+1}$ bijectively onto the $k+1$ vertices of $\Delta_k$.
Paul Erdős, Some unsolved problems , Michigan Math. J. 4
1957
Earlier work this paper cites.
Victor Klee, Unsolved problems in intuitive geometry , 1960, Hectographical lecture notes, Seatle
1960
Earlier work this paper cites.
L. Danzer and B. Grünbaum, Über zwei Probleme bezüglich konvexer Körper von P. Erdős und von V. L. Klee , Math. Z. 79
1962
Earlier work this paper cites.
Branko Grünbaum, Strictly antipodal sets , Israel J. Math. 1
1963
Earlier work this paper cites.
Michael L. Fredman and János Komlós, On the size of separating systems and families of perfect hash functions , SIAM J. Algebraic Discrete Methods 5
1984
Earlier work this paper cites.
J. Körner and K. Marton, New bounds for perfect hashing via information theory , European J. Combin. 9
1988
Earlier work this paper cites.
by same author, Convex polytopes , second ed., Graduate Texts in Mathematics, vol. 221, Springer-Verlag, New York, 2003, Prepared and with a preface by Volker Kaibel, Victor Klee and Günter M. Ziegler. MR 1976856
2003
Earlier work this paper cites.
Howard Barnum and Alexander Wilce, Information processing in convex operational theories , Electronic Notes in Theoretical Computer Science 270
2008
Cited alongside, same era.
Peter Janotta and Raymond Lal, Generalized probabilistic theories without the no-restriction hypothesis , Phys. Rev. A 87
2013
Cited alongside, same era.
Koenraad M. R. Audenaert and Milán Mosonyi, Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination , J. Math. Phys. 55
2014
Cited alongside, same era.
Imre Bárány, Tensors, colours, octahedra , Geometry, structure and randomness in combinatorics, CRM Series, vol. 18, Ed. Norm., Pisa, 2015, pp. 1–17. MR 3362294
2015
Cited alongside, same era.
Balázs Gerencsér and Viktor Harangi, Acute sets of exponentially optimal size , Discrete Comput. Geom. 62
2019
Dmitriy Zakharov, Acute sets , Discrete Comput. Geom. 61
2019
Later among the works it cites.
Martin Plávala, General probabilistic theories: An introduction , 2021
2021
Later among the works it cites.
Chaoping Xing and Chen Yuan, Beating the probabilistic lower bound on perfect hashing , Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA), [Society for Industrial and Applied Mathematics (SIAM)], Philadelphia, PA, 2021, pp. 33–41. MR 4262436
2021
Later among the works it cites.
Stefano Della Fiore, Simone Costa, and Marco Dalai, Improved bounds for (b, k)-hashing , IEEE Transactions on Information Theory 68
2022
Later among the works it cites.
Ludovico Lami, Daniel Goldwater, and Gerardo Adesso, A post-quantum associative memory , Journal of Physics A: Mathematical and Theoretical 56
2023
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
by same author, Too acute to be true: the story of acute sets , Amer. Math. Monthly 126
2019
Cited alongside, same era.
Mihály Weiner, Realization of an arbitrary structure of perfect distinguishability of states in general probability theory , 2023
2023
Closest in time.