Related papers: Semifields, relative difference sets, and bent fun…
We give an account on what is known on the subject of permutation matchings, which are bijections of a finite regular semigroup that map each element to one of its inverses. This includes partial solutions to some open questions, including…
We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are introduced. Distinction between commutative and…
The concept of differential uniformity was recently extended to the $c$-differential uniformity. An interesting problem in this area is the construction of functions with low $c$-differential uniformity and a lot of research has been done…
Planar functions over finite fields give rise to finite projective planes. They were also used in the constructions of DES-like iterated ciphers, error-correcting codes, and codebooks. They were originally defined only in finite fields with…
In this article, we study algebraic decompositions and secondary constructions of almost perfect nonlinear (APN) functions. In many cases, we establish precise criteria which characterize when certain modifications of a given APN function…
Inverse semigroups are a class of semigroups whose structure induces a compatible partial order. This partial order is examined so as to establish mirror properties between an inverse semigroup and the semilattice of its idempotent…
Every (left) linear function on a subspace of a finite-dimensional vector space over a (skew) field can be extended to a (left) linear function on the whole space. This paper explores the extent to what this basic fact of linear algebra is…
Skew idempotent functionals of ordered semirings are studied. Different associative and non-associative semirings are considered. Theorems about properties of skew idempotent functionals are proved. Examples are given.
The Menichetti-Kaplansky theorem states that a finite semifield that is three-dimensional over its center is either a field or a twisted field of Albert. This implies that a quadratic homogeneous bijection of $\mathbb{P}^2(\mathbb{F}_q)$ is…
Inspired by a recent work of Mesnager, we present several new infinite families of quadratic ternary bent, near-bent and 2-plateaued functions from some known quadratic ternary bent functions. Meanwhile, the distribution of the Walsh…
Model sets (also called cut and project sets) are generalizations of lattices, and multi-component model sets are generalizations of lattices with colourings. In this paper, we study self-similarities of multi-component model sets. The main…
This paper characterizes which subsets of C^n can be the set of positions of n points on a linkage in the complex plane C. For example, assuming compactness they are just compact semialgebraic sets. Noncompact configuration spaces are…
This article serves as an introduction to several recent developments in the study of quasisymmetric functions. The focus of this survey is on connections between quasisymmetric functions and the combinatorial Hopf algebra of noncommutative…
This work presents a novel approach for semi-supervised semantic segmentation. The key element of this approach is our contrastive learning module that enforces the segmentation network to yield similar pixel-level feature representations…
In the present paper a new concept of representability is introduced, which can be applied to not total and also to intransitive relations (semiorders in particular). This idea tries to represent the orderings in the simplest manner,…
The representations of dimension vector $\alpha$ of the quiver Q can be parametrised by a vector space $R(Q,\alpha)$ on which an algebraic group $\Gl(\alpha)$ acts so that the set of orbits is bijective with the set of isomorphism classes…
Bent functions as optimal combinatorial objects are difficult to characterize and construct. In the literature, bent idempotents are a special class of bent functions and few constructions have been presented, which are restricted by the…
We construct infinite classes of almost bent and almost perfect nonlinear polynomials, which are affinely inequivalent to any sum of a power function and an affine function.
We define supersymmetric zeta functions and supersymmetric determinants, which can reveal spectral properties complementary to those captured by the supersymmetric indices. They play a crucial role in analyzing the Cardy-like behaviors of…
A conjecturally complete list of connected components of complements of discriminant varieties (aka wave fronts) of smooth function singularities of type $X_{10}^3$ and $X_{10}^1$ is presented; it are the first examples of not…