Related papers: On Gluck's conjecture
In this article we determine the implicational fragments of most of the known subintuitionistic logics.
In this note we provide a new, algebraic proof of the excessive Laurent phenomenon for mutations of potentials (in the sense of [Galkin S., Usnich A., Preprint IPMU 10-0100, 2010]) by introducing to this theory the analogue of the upper…
The main purpose of the paper is the proof of a cardinal inequality for a space with points $G_\delta$, obtained with the help of a long version of the Menger game. This result improves a similar one of Scheepers and Tall.
We obtain new lower and upper bounds for probabilities of unions of events.These bounds are sharp. They are stronger than earlier ones. General bounds maybe applied in arbitrary measurable spaces.We have improved the method that has been…
A new bound for the rank of the intersection of finitely generated subgroups of a free group is given, formulated in topological terms, and very much in the spirit of Stallings. The bound is a contribution to (although unfortunately not a…
Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. In this paper, we obtain upper bounds for the Castelnuovo-Mumford regularity of $I(G)^q$ in terms of certain combinatorial invariants associated with $G$. We…
In this paper we give a short, new proof of a natural generalization of Gerzon's bound. This bound improves the Delsarte, Goethals and Seidel's upper bound in a special case. Our proof is a simple application of the linear algebra bound…
A conjecture of Talagrand (2010) states that the so-called expectation and fractional expectation thresholds are always within at most some constant factor from each other. In this note we generalize a method of DeMarco and Kahn and settle…
In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.
In this paper, we prove a conjecture proposed by George Beck, which involves gap-free partitions and partitions with distinct parts.
Bounds for the maximal degree of certain Gr\"obner bases of simplicial toric ideals are given. These bounds are close to the bound stated in Eisenbud-Goto's Conjecture on the Castelnuovo-Mumford regularity.
We study two kinds of conjectural bounds for the prime gap after the k-th prime $p_k$: (A) $p_{k+1} < (p_k)^{1+1/k}$ and (B) $p_{k+1}-p_k < \log^2 p_k - \log p_k - b$ for $k>9$. The upper bound (A) is equivalent to Firoozbakht's conjecture.…
The paper presents a counterexample to the Hodge conjecture.
In this paper, we prove a conjecture of Schnell in the surface case.
In this paper, we get the sharp bound for $|G/O_p(G)|_p$ under the assumption that either $p^2 \nmid \chi(1)$ for all $\chi \in {\rm Irr}(G)$ or $p^2 \nmid \phi(1)$ for all $\phi \in {\rm IBr}_p(G)$. This would settle two conjectures raised…
We propose a conjectural formula for $DR_g(a,-a) \lambda_g$ and check all its expected properties. Our formula refines the one point case of a similar conjecture made by the first named author in collaboration with Gu\'er\'e and Rossi, and…
We give a new proof of a_4\phi_3 summation due to G.E. Andrews and confirm another_4\phi_3 summation conjectured by him recently. Some variations of these two_4\phi_3 summations are also given.
In this paper I prove a conjecture which gives a lower bound for the largest absolute value of the coefficients of the n-th cyclotomic polynomial for some n. Moreover this estimate is essentially sharp.
This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.
A conjecture regarding the structure of expander graphs is discussed.