Related papers: A refinement of Horn's conjecture

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

We study the open refined topological string amplitudes using the refined topological vertex. We determine the refinement of holonomies necessary to describe the boundary conditions of open amplitudes (which in particular satisfy the…

In this paper we improve drastically the estimate for the multiplicity of a binary recurrence. The main contribution comes from an effective version of the Faltings' Product Theorem.

We prove a conjecture by Kreiman and Lakshmibai on a combinatorial description of multiplicities of points on Schubert varieties in Graszmannians in terms of certain sets of reflections in the corresponding Weyl group. The proof is…

We study algebras on which the Berenstein-Zelevinsky conjecture is true. In particular, we prove that this conjecture is true "up to localization".

In this paper, we provide a probabilistic interpretation of the Volkenborn integral; this allows us to extend results by T. Kim et al about sums of Euler numbers to sums of Bernoulli numbers. We also obtain a probabilistic representation of…

In the last two decades about a dozen methods were invented which derive, from a series of composite spectra over the orbit, the spectra of individual components in binary and multiple systems. Reconstructed spectra can then be analyzed…

Recently, very interesting results have been obtained concerning the Fourier spectra of power permutations over a finite field. In this note we survey the recent ideas of Aubry, Feng, Katz, and Langevin, and we pose new open problems…

This note is to indicate the new sphere of applicability of the method developed by Mlak as well as by the author. Restoring those ideas is summoned by current developments concerning $K$-spectral sets on numerical ranges.

In a very celebrated paper A. Connes has formulated a conjecture which is now one of the most important open problem in Operator Algebras. This importance comes from the works of many mathematicians who have found some unexpected equivalent…

We investigate permutations in terms of their cycle structure and descent set. To do this, we generalize the classical bijection of Gessel and Reutenauer to deal with permutations that have some ascending and some descending blocks. We then…

In this paper, we establish a refined transversality theorem on linear perturbations from a new perspective of Hausdorff measures. Furthermore, we give its applications not only to singularity theory but also to multiobjective optimization.

We explicitly determine the Ap\'ery limits for the sums of powers of binomial coefficients. As an application, we prove a weak version of Franel's conjecture on the order of the recurrences for these sequences. Namely, we prove the…

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

Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.

In this paper we want to revisit results of Dahmen and Micchelli on box-splines which we reinterpret and make more precise. We compare these ideas with the work of Brion, Szenes, Vergne and others on polytopes and partition functions.

In this paper we study subsets $E$ of ${\Bbb Z}_p^d$ such that any function $f: E \to {\Bbb C}$ can be written as a linear combination of characters orthogonal with respect to $E$. We shall refer to such sets as spectral. In this context,…

In this paper we give a conjectural refinement of the Davenport-Heilbronn theorem on the density of cubic field discriminants. We explain how this refinement is plausible theoretically and agrees very well with computational data.

We extend the Heine-Stieltjes Theorem to concern all (non-degenerate) differential operators preserving the property of having only real zeros. This solves a conjecture of B. Shapiro. The new methods developed are used to describe intricate…

We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.