Related papers: A short proof that all linear codes are weakly alg…
Every absolutely summing linear operator is weakly compact. However, for strongly summing multilinear operators and polynomials - one of the most natural extensions of the linear case to the non linear framework - weak compactness does not…
We give a short proof of Chevalley's theorem that every algebraic group is an extension of an Abelian variety by a linear algebraic group. Along the way we treat Bertini's irreducibility theorem.
In a 2022, Bartoli, Cossidente, Marino, and Pavese proved that in the projective space ${\rm PG}(3,q^3)$, one can find three $\mathbb F_q$-subgeometries such that the union of their point sets is a strong blocking set. This proves the…
We present an $O(n\log n)$-time algorithm that determines whether a given planar $n$-gon is weakly simple. This improves upon an $O(n^2\log n)$-time algorithm by Chang, Erickson, and Xu (2015). Weakly simple polygons are required as input…
We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly…
Using a coupling argument, we establish a general weak law of large numbers for functionals of binomial point processes in d-dimensional space, with a limit that depends explicitly on the (possibly non-uniform) density of the point process.…
We investigate the geometry of the support of small weight codewords of dual algebraic geometric codes on smooth complete intersections by applying the powerful tools recently developed by Alain Couvreur. In particular, by restricting…
We design a polynomial time decoding algorithm for linearized Algebraic Geometry codes with unramified evaluation places, a family of sum-rank metric evaluation codes on division algebras over function fields. By establishing a Serre…
Observations in quantum weak measurements are determined by complex numbers called weak values. We present a geometrical interpretation of the argument of weak values of general Hermitian observables in $N$-dimensional quantum systems in…
We study systems of equations over graphs, posets and matroids. We give the criteria, when a direct power of such algebraic structures is equationally Noetherian. Moreover we prove that any direct power of a finite algebraic structure is…
We provide a theoretical study of Algebraic Geometry codes constructed from abelian surfaces defined over finite fields. We give a general bound on their minimum distance and we investigate how this estimation can be sharpened under the…
A weak metric on a set is a function that satisfies the axioms of a metric except the symmetry and the separation axioms. In the present paper we introduced a weak metric, called the Apollonian weak metric, on any subset of a Euclidean…
The goal of this paper is to prove that several variants of deciding whether a poset can be (weakly) embedded into a small Boolean lattice, or to a few consecutive levels of a Boolean lattice, are NP-complete, answering a question of Griggs…
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…
The Grassmannian is an important object in Algebraic Geometry. One of the many techniques used to study the Grassmannian is to build a vector space from its points in the projective embedding and study the properties of the resulting linear…
We construct algebraic geometric codes from weak del Pezzo surfaces. The codes are associated to the anti-canonical class of the anti-canonical model and to the set of rational points of these models. Since we consider weak Del Pezzo…
An artinian graded algebra, $A$, is said to have the Weak Lefschetz property (WLP) if multiplication by a general linear form has maximal rank in every degree. A vast quantity of work has been done studying and applying this property,…
The class of weak BCK-algebras is obtained by weakening one of standard BCK axioms. It is known that every weak BCK-algebra is completely determined by the structure of its initial segments. We review several natural classes of commutative…
I. P. Goulden, S. Litsyn, and V. Shevelev [On a sequence arising in algebraic geometry, J. Integer Sequences 8 (2005), 05.4.7] conjectured that certain Laurent polynomials associated with the solution of a functional equation have only odd…
The minimum distance is one of the most important combinatorial characterizations of a code. The maximum likelihood decoding problem is one of the most important algorithmic problems of a code. While these problems are known to be hard for…