Related papers: A refinement of Horn's conjecture
Comon's conjecture on the equality of the rank and the symmetric rank of a symmetric tensor, and Strassen's conjecture on the additivity of the rank of tensors are two of the most challenging and guiding problems in the area of tensor…
Brand, Nanongkai, and Saranurak introduced a conjecture known as the Hinted Mv Conjecture. Although it was originally formulated for the matrix case, we generalize it here to the tensor setting.
We provide several simple recursive formulae for the moment sequence of infinite Bernoulli convolution. We relate moments of one infinite Bernoulli convolution with others having different but related parameters. We give examples relating…
A method is suggested for obtaining the Plancherel measure for Affine Hecke Algebras as a limit of integral-type formulas for inner products in the polynomial and related modules of Double Affine Hecke Algebras. The analytic continuation…
The Sinc convolution is an approximate formula for indefinite convolutions proposed by Stenger. The formula was derived based on the Sinc indefinite integration formula combined with the single-exponential transformation. Although its…
In this paper we reformulate some results obtained by Heisenberg into modern mathematical language of honeycombs. This language was developed in connection with complete solution of the Horn conjecture problem. Such a reformulation is done…
We use a spectral theory perspective to reconsider properties of the Riemann zeta function. In particular, new integral representations are derived and used to present its value at odd positive integers.
We study a generalization of the notion of conservativity spectrum of an arithmetical theory to a language with transfinitely many truth definitions. We establish a correspondence of conservativity spectra and points of a generalized…
We give a reformulation of the Lehmer conjecture about algebraic integers in terms of a simple counting problem modulo p.
We realize that geometric polynomials and p-Bernoulli polynomials and numbers are closely related with an integral representation. Therefore, using geometric polynomials, we extend some properties of Bernoulli polynomials and numbers such…
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
We prove a number of conjectures [arXiv:2005.04066] recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence.
We develop techniques to deal with monotonicity of sequences z_{n+1}/z_n and \sqrt[n]{z_n}. A series of conjectures of Zhi-Wei Sun and of Amdeberhan et al. are verified in certain unified approaches.
We introduce some generalized topological concepts to deal with union-closed families, and show that one can reduce the proof of Frankl's conjecture to some families of so-called supratopological spaces. We prove some results on the…
Halperin has conjectured that the Serre spectral sequence of any fibration that has fibre space a certain kind of elliptic space should collapse at the E_2-term. In this paper we obtain an equivalent phrasing of this conjecture, in terms of…
We present a slightly simpler proof of the multilinear refined Strichartz estimate, and prove a slightly more general linear refined Strichartz estimate. Our arguments seek to clarify the connection between these estimates, refined…
We provide a geometric proof of the Schubert calculus interpretation of the Horn conjecture, and show how the saturation conjecture follows from it. The geometric proof gives a strengthening of Horn and saturation conjectures. We also…
Fuglede's conjecture states that a subset $\Omega\subseteq\mathbb{R}^{n}$ of positive and finite Lebesgue measure is a spectral set if and only if it tiles $\mathbb{R}^{n}$ by translation. The conjecture does not hold in both directions for…
We expand upon some topics reviewed and sketched in a book to appear with more details, embellishments, and some new material of a speculative nature.
In this paper, we refine the function $g(x)$ on Grimm's conjecture and improve a result of Erd\"{o}s and Selfridge without using Hall's theorem.