[图书][B] Using the Borsuk-Ulam theorem: lectures on topological methods in combinatorics and geometry
J Matoušek, A Björner, GM Ziegler - 2003 - Springer
A number of important results in combinatorics, discrete geometry, and theoretical computer
science have been proved using algebraic topology. While the results are quite famous …
science have been proved using algebraic topology. While the results are quite famous …
The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg
J De Loera, X Goaoc, F Meunier, N Mustafa - Bulletin of the American …, 2019 - ams.org
We discuss five fundamental results of discrete mathematics: the lemmas of Sperner and
Tucker from combinatorial topology and the theorems of Carathéodory, Helly, and Tverberg …
Tucker from combinatorial topology and the theorems of Carathéodory, Helly, and Tverberg …
A user's guide to the topological Tverberg conjecture
AB Skopenkov - Russian Mathematical Surveys, 2018 - iopscience.iop.org
The well-known topological Tverberg conjecture was considered a central unsolved
problem of topological combinatorics. The conjecture asserts that for any integers $ r $, $ d …
problem of topological combinatorics. The conjecture asserts that for any integers $ r $, $ d …
Helly-type problems
In this paper we present a variety of problems in the interface between combinatorics and
geometry around the theorems of Helly, Radon, Carathéodory, and Tverberg. Through these …
geometry around the theorems of Helly, Radon, Carathéodory, and Tverberg. Through these …
Tverberg's theorem is 50 years old: a survey
This survey presents an overview of the advances around Tverberg's theorem, focusing on
the last two decades. We discuss the topological, linear-algebraic, and combinatorial …
the last two decades. We discuss the topological, linear-algebraic, and combinatorial …
Tverberg plus constraints
PVM Blagojević, F Frick… - Bulletin of the London …, 2014 - academic.oup.com
Many of the strengthenings and extensions of the topological Tverberg theorem can be
derived with surprising ease directly from the original theorem: For this, we introduce a proof …
derived with surprising ease directly from the original theorem: For this, we introduce a proof …
Beyond the Borsuk–Ulam theorem: the topological Tverberg story
PVM Blagojević, GM Ziegler - A Journey Through Discrete Mathematics: A …, 2017 - Springer
Bárány's “topological Tverberg conjecture” from 1976 states that any continuous map of an
N-simplex Δ N Δ _ N to ℝ d R^ d, for N≥(d+ 1)(r− 1), maps points from r disjoint faces in Δ N …
N-simplex Δ N Δ _ N to ℝ d R^ d, for N≥(d+ 1)(r− 1), maps points from r disjoint faces in Δ N …
Counterexamples to the topological Tverberg conjecture
F Frick - arXiv preprint arXiv:1502.00947, 2015 - arxiv.org
The" topological Tverberg conjecture" by B\'ar\'any, Shlosman and Sz\H {u} cs (1981) states
that any continuous map of a simplex of dimension $(r-1)(d+ 1) $ to $\mathbb {R}^ d $ maps …
that any continuous map of a simplex of dimension $(r-1)(d+ 1) $ to $\mathbb {R}^ d $ maps …
Barycenters of polytope skeleta and counterexamples to the topological Tverberg conjecture, via constraints
PVM Blagojević, F Frick, GM Ziegler - Journal of the European …, 2019 - ems.press
Barycenters of polytope skeleta and counterexamples to the Topological Tverberg Conjecture,
via constraints Page 1 DOI 10.4171/JEMS/881 J. Eur. Math. Soc. 21, 2107–2116 c European …
via constraints Page 1 DOI 10.4171/JEMS/881 J. Eur. Math. Soc. 21, 2107–2116 c European …
Tverberg's theorem at 50: extensions and counterexamples
I Bárány, PVM Blagojevic, GM Ziegler - Notices of the AMS, 2016 - ams.org
We describe how a powerful new “constraint method” yields many different extensions of the
topological version of Tverberg's 1966 Theorem in the prime power case—and how the …
topological version of Tverberg's 1966 Theorem in the prime power case—and how the …