Related papers: Two Lorentzian Lattices
In this paper we prove that given any two point lattices $\Lambda_1 \subset \mathbb{R}^n$ and $ \Lambda_2 \subset \nobreak \mathbb{R}^{n-k}$, there is a set of $k$ vectors $\bm{v}_i \in \Lambda_1$ such that $\Lambda_2$ is, up to similarity,…
In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
In this paper we study the capacity of Lorentzian polynomials. We give a new proof of a theorem of Br\"and\'en, Leake and Pak. Our approach is probabilistic in nature and uses a lemma about a certain distance of binomial distributions to…
We report on a test of the Maldacena conjecture. This string/field theory correspondence has interesting applications. When combined with Rehren's theorem, it has implications for issues concerning space-time structure and Lorentz symmetry.…
We study certain lattices constructed from finite abelian groups. We show that such a lattice is eutactic, thereby confirming a conjecture by B\"ottcher, Eisenbarth, Fukshansky, Garcia, Maharaj. Our methods also yield simpler proofs of two…
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.
In this paper we prove the validity of a formula for computing the Alexander invariant which was originally conjectured by Bar-Natan and Dancso in [BND].
Recently three proofs of the $A_2$-conjecture were obtained. All of them are "glued" to euclidian space and a special choice of one random dyadic lattice. We build a random "dyadic" lattice in any doubling metric space which have properties…
We are motivated by a result of Alzer and Luca who presented all the integer solutions to the relations $(k!)^n-k^n=(n!)^k-n^k$ and $(k!)^n+k^n=(n!)^k+n^k$. We modify the equations by considering the double factorial instead and present all…
Simion conjectured the unimodality of a sequence counting lattice paths in a grid with a Ferrers diagram removed from the northwest corner. Recently, Hildebrand and then Wang proved the stronger result that this sequence is actually log…
We give a new demonstration of Loewner's characterization of polynomials, solving in the positive a conjecture proposed by Laird and McCann in 1984.
We give new proofs on Arnold Chord Conjecture and Weinstein Conjecture in M\times C which generalizes the previous works.
This paper presents the best known bounds for a conjecture of Gluck and a conjecture of Navarro.
We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.
We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.
In this paper we prove the WALA conjecture.
In this paper, we completely classify three-dimensional Lorentzian $Ein(2)$ Lie groups.
This is Part A of four Parts dedicated to modular lattices of finite length. It builds on 1992 notes of the author (available on ResearchGate), and in so doing heeds a wish of the late Gian-Carlo Rota. Part A is in fairly final form and…
The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.