相关论文: Counterexamples to Okounkov's Log-Concavity Conjec…

We show that normalized Schur polynomials are strongly log-concave. As a consequence, we obtain Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients in the special case of Kostka numbers.

We formulate a series of conjectures on the stable tensor product of irreducible representations of symmetric groups, which are closely related to the reduced Kronecker coefficients. These conjectures are certain generalizations of…

We give a counterexample to the PIA (precise inversion of adjunction) conjecture for minimal log discrepancies. We also give a counterexample to the LSC conjecture for families.

We prove Okounkov's conjecture, a conjecture of Fomin-Fulton-Li-Poon, and a special case of Lascoux-Leclerc-Thibon's conjecture on Schur positivity and give several more general statements using a recent result of Rhoades and Skandera. An…

In this short note we present a family of counterexamples to the King's conjecture.

We give a counterexample of Morrison's cone conjecture for a strict Calabi-Yau threefold.

In this paper, we give a simple counter example to the famous Hodge conjecture.

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

We derive a family of $L^p$ estimates of the X-Ray transform of positive measures in $\mathbb R^d$, which we use to construct a $\log R$-loss counterexample to the Mizohata-Takeuchi conjecture for every $C^2$ hypersurface in $\mathbb R^d$…

We give a new formula for the Littlewood--Richardson coefficients in terms of peelable tableaux compatible with shuffle tableaux, in the same fashion as Remmel--Whitney rule. This gives an efficient way to compute generalized…

In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.

The paper presents a counterexample to the Hodge conjecture.

In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

We give a closed formula of the Littlewood-Richardson coefficients.

Using calculus we show how to prove some combinatorial inequalities of the type log-concavity or log-convexity. It is shown by this method that binomial coefficients and Stirling numbers of the first and second kinds are log-concave, and…

We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.

We give a counterexample to the most optimistic analogue (due to Kleshchev and Ram) of the James conjecture for Khovanov-Lauda-Rouquier algebras associated to simply-laced Dynkin diagrams. The first counterexample occurs in type A_5 for p =…