Related papers: On two Kuznetsov's conjectures
In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.
In this paper we extend some results obtained by Artamonov and Sabitov for quantum polynomials to skew quantum polynomials and quasi-commutative bijective skew PBW extensions. Moreover, we find a counterexample to the conjecture proposed in…
We provide a short proof of the 1-dimensional flat chain conjecture.
In a recent work Brevik \emph{et al.} have offered formal proofs of two results which figure prominently in calculations of the Casimir pressure on a sphere. It is shown by means of simple counterexamples that each of those proofs is…
We look at an old conjecture of A. Tarski on cardinal arithmetic and show that if a counterexample exists, then there exists one of length omega_1 + omega .
We show that there is a knot satisfying the property that for each minimal crossing number diagram of the knot and each single crossing of the diagram, changing the crossing results in a diagram for a knot whose unknotting number is at…
We give an explicit counterexample to the Bunkbed Conjecture introduced by Kasteleyn in 1985. The counterexample is given by a planar graph on $7222$ vertices, and is built on the recent work of Hollom (2024).
Analogues of Kolmogorov comparison theorems and some of their applications were established.
We give new proofs on Arnold Chord Conjecture and Weinstein Conjecture in M\times C which generalizes the previous works.
It is proven that for any system of n points z_1, ..., z_n on the (complex) unit circle, there exists another point z of norm 1, such that $$\sum 1/|z-z_k|^2 \leq n^2/4.$$ Equality holds iff the point system is a rotated copy of the nth…
When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof…
Reply to the recent comment by I.Ispolatov and M.Karttunen, cond-mat/0303564
This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.
This paper contains the proof of difference counterparts of the conjectures due to Keven Kadell on symmetric and anti-symmetric Macdonald polynomials.
We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.
In this paper, we present a minimal counterexample to a conjecture of Perles that answers a question of Haase and Ziegler. The example is a simple 4-polytope that has an induced 3-connected 3-regular subgraph, whose graph complement is…
The following is a concise exposition of the conjecture and three of its proofs for the case of positive entropy by D. Rudolph [22] , B. Host [14] and W. Parry [21]. A simpler theorem of R. Lyons [19] - preceding them - is also presented…
We point out that a concise proof of Theorem 2 in the article, 'On a quadratic estimate of Shafer' by L. Zhu contains a small mistake. Correcting this mistake and giving alternative proofs of Theorem 2 is the main aim of this note.
We continue to discuss the example presented in \cite{JarPfl2015}. In particular, we clarify some gaps and complete the description of the Shilov boundary.
Question when rectangle can be tiled with similar copies of rectangles witch quetient of sides quadratic irrationalities. New proof of one part F. Sharov's theorem. Other close result.