Related papers: On Ryser's Conjecture

We give some results and conjectures about recurrence relations for certain sequences of binomial sums.

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

In this note, we revisit a classical problem related to the density of nonlinear statistics. We obtain a new representation of densities and, for the first time, a necessary and sufficient condition for the existence of densities is…

We prove a variation of Gronwall's lemma.

We prove that the Thin Sandwich Conjecture in general relativity is valid, provided that the data $(g_{ab},\dot g_{ab})$ satisfy certain geometric conditions. These conditions define an open set in the class of possible data, but are not…

We talk about the image of the Hilbert map. We show the necessary and sufficient condition that the Hilbert map is surjective.

We show the Graceful Tree Conjecture holds.

The necessary and suffcient condition for a set of matrices to commute is given and proven.

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.

After having shown that the formula which describes the Doppler effect in the general case holds only in the case of the "very high" frequency assumption, we derive free of assumptions Doppler formulas for two scenarios presented in the…

We extend Carleson's interpolation Theorem to sequences of matrices, by giving necessary and sufficient separation conditions for a sequence of matrices to be interpolating.

We give a new proof of Chen-Lin result with Li-Zhang method.

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

We give a sufficient condition for the strong symmetric version of Strassen's additivity conjecture: the Waring rank of a sum of forms in independent variables is the sum of their ranks, and every Waring decomposition of the sum is a sum of…

We obtain new partial results supporting the spectral set conjecture in dimension 1.

This is a survey on Kawaguchi-Silverman conjecture.

We provide a sufficient condition for sets of mobile sampling in terms of the surface density of the set.

Pati (Physics Letters A, 2000) derived a sufficient condition for the existence of Schmidt decomposition in tripartite Hilbert spaces. In this paper, we show that the condition is erroneous by demonstrating some counter-examples. Moreover,…

The perturbation theory based on typicality introduced in Ref. [1] and further refined in Refs. [2, 3] provides a powerful tool since it is intended to be applicable to a wide range of scenarios while relying only on a few parameters. Even…

This paper presents new sufficient and equivalent conditions for the generalized version of the Riemann Hypothesis. The paper derives also statements and remarks concerning zero-free regions, modified Hadamard-product formulas and the…