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08/09/2023
Cycles in graphs and in hypergraphs
This is an expository paper. A 1-cycle in a graph is a set C of edges su...
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08/05/2022
To the Kühnel conjecture on embeddability of k-complexes in 2k-manifolds
The classical Heawood inequality states that if the complete graph K_n o...
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12/06/2021
Embeddings of k-complexes in 2k-manifolds and minimum rank of partial symmetric matrices
Let K be a k-dimensional simplicial complex having n faces of dimension ...
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07/29/2021
Simple proofs of estimations of Ramsey numbers and of discrepancy
In this expository note we present simple proofs of the lower bound of R...
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06/26/2021
A short exposition of the Patak-Tancer theorem on non-embeddability of k-complexes in 2k-manifolds
In 2019 P. Patak and M. Tancer obtained the following higher-dimensional...
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05/02/2021
A structured proof of the Kolmogorov superposition theorem
We present a well-structured detailed exposition of a well-known proof o...
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08/06/2020
Some `converses' to intrinsic linking theorems
A low-dimensional version of our main result is the following `converse'...
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08/02/2020
Extendability of simplicial maps is undecidable
We present a short proof of the Čadek-Krčál-Matoušek-Vokřínek-Wagner res...
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01/06/2020
A user's guide to basic knot and link theory
This paper is expository and is accessible to students. We define simple...
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08/23/2019
Stronger counterexamples to the topological Tverberg conjecture
Denote by Δ_N the N-dimensional simplex. A map fΔ_N→R^d is an almost r-e...
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08/25/2018
A short exposition of S. Parsa's theorems on intrinsic linking and non-realizability
We present a short exposition of the following results by S. Parsa. Le...
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08/25/2018
A short exposition of S. Parsa's theorem on intrinsic linking and non-realizability
We present a short statement and proof of the following result by S. Par...
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05/25/2018