Related papers: Classifications and constructions of minimum size …

We examine a family of discrete second-order systems which are integrable through reduction to a linear system. These systems were previously identified using the singularity confinement criterion. Here we analyse them using the more…

We prove that suitably generic pairs of linear equations on an even number of variables are uncommon. This verifies a conjecture of Kam\v{c}ev, Morrison and the second author. Moreover, we prove that any large system containing such a…

Lunardon and Polverino introduced in 2001 a new family of maximum scattered linear sets in $\mathrm{PG}(1,q^n)$ to construct linear minimal R\'edei blocking sets. This family has been extended first by Lavrauw, Marino, Trombetti and…

In this paper, we establish a common fixed point theorem for two pairs of occasionally weakly compatible single and set-valued maps satisfying a strict contractive condition in a metric space. Our result extends many results existing in the…

Linearized polynomials appear in many different contexts, such as rank metric codes, cryptography and linear sets, and the main issue regards the characterization of the number of roots from their coefficients. Results of this type have…

In this paper, we study KM-arcs of type t, i.e. point sets of size q + t in PG(2, q) such that every line contains 0, 2 or t of its points. We use field reduction to give a different point of view on the class of translation arcs. Starting…

We study the problem of recovering a structured signal from independently and identically drawn linear measurements. A convex penalty function $f(\cdot)$ is considered which penalizes deviations from the desired structure, and signal…

Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, secure two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then…

We introduce Fermi Sets, a universal and physically interpretable neural architecture for fermionic many-body wavefunctions. Building on a ``parity-graded'' representation [1], we prove that any continuous fermionic wavefunction on a…

In this paper we study the minimal faithful permutation representations of $SL_n(\mathbb F_q)$ and $GL_n(\mathbb F_q)$.

Let $\mathrm{PG}(1,E)$ be the projective line over the endomorphism ring $E=End_q({\mathbb F}_{q^t})$ of the $\mathbb F_q$-vector space ${\mathbb F}_{q^t}$. As is well known there is a bijection $\Psi:\mathrm{PG}(1,E)\rightarrow{\cal…

Let f(x_1,x_2,...,x_m) = u_1x_1+u_2 x_2+... + u_mx_m be a linear form with positive integer coefficients, and let N_f(k) = min{|f(A)| : A \subseteq Z and |A|=k}. A minimizing k-set for f is a set A such that |A|=k and |f(A)| = N_f(k). A…

We completely classify all minimal problems for Structure-from-Motion (SfM) where arrangements of points and lines are fully observed by multiple uncalibrated pinhole cameras. We find 291 minimal problems, 73 of which have unique solutions…

For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…

A critical set in an $n \times n$ Latin square is a minimal set of entries that uniquely identifies it among all Latin squares of the same size. It is conjectured by Nelder in 1979, and later independently by Mahmoodian, and Bate and van…

For every complex number $x$, let $\Vert x\Vert_{\mathbb{Z}}:=\min\{|x-m|:\ m\in\mathbb{Z}\}$. Let $K$ be a number field, let $k\in\mathbb{N}$, and let $\alpha_1,\ldots,\alpha_k$ be non-zero algebraic numbers. In this paper, we completely…

Under the assumption of the minimal model theory for projective klt pairs of dimension $n$, we establish the minimal model theory for lc pairs $(X/Z,\Delta)$ such that the log canonical divisor is relatively log abundant and its restriction…

In this paper we study observation problem for linear 2-point BVP Dx=Bf assuming that information about system input f and random noise \eta in system state observation model y=Hx+\eta$ is incomplete (f and M\eta\eta' are some arbitrary…

We formulate a conjecture on the behavior of the minimal free resolutions of sets of general points on arbitrary varieties embedded by complete linear series, in analogy with the well-known Minimal Resolution Conjecture for points in…

We provide a complete classification, in the language of weak-combinatorics, of minimal plus-one generated line arrangements in the complex projective plane with double and triple intersection points.