Related papers: Perspicacious $l_p$ norm parameters

Let $\Delta$ be a numerical semigroup and let $d\ge 2$ be an integer. We study the fiber of the quotient map \(S\mapsto S/d\) over $\Delta$. We describe its elements as semigroups of the form $\langle X\rangle+d\Delta$, for suitable finite…

An algebraic structure is said to be congruence permutable if its arbitrary congruences $\alpha$ and $\beta$ satisfy the equation $\alpha \circ \beta =\beta \circ \alpha$, where $\circ$ denotes the usual composition of binary relations. For…

We study the cyclotomic exponent sequence of a numerical semigroup $S,$ and we compute its values at the gaps of $S,$ the elements of $S$ with unique representations in terms of minimal generators, and the Betti elements $b\in S$ for which…

For an asymptotic $\ell_1$ space $X$ with a basis $(x_i)$ certain asymptotic $\ell_1$ constants, $\delta_\alpha (X)$ are defined for $\alpha <\omega_1$. $\delta_\alpha (X)$ measures the equivalence between all normalized block bases…

For a nonnegative integer $p$, the $p$-numerical semigroup $S_p$ is defined as the set of integers whose nonnegative integral linear combinations of given positive integers $a_1,a_2,\dots,a_\kappa$ with $\gcd(a_1,a_2,\dots,a_\kappa)=1$ are…

For a group $G$, we define a graph $\Delta(G)$ by letting $G^{\#} = G \setminus \{ 1 \}$ be the set of vertices and by drawing an edge between distinct elements $x,y\in G^{\#}$ if and only if the subgroup $\langle x,y\rangle$ is cyclic.…

In this article, first we give two formulae for the delta invariant of a complex curve singularity that can be embedded as a ${\mathbb Q}$-Cartier divisor in a normal surface singularity with rational homology sphere link. Next, we consider…

Let $X$ be a nonempty set, and let $\mathcal{T}_X$ be the full transformation semigroup on $X$. For a partition $\mathcal{P} = \{X_i \;|\; i\in I\}$ of $X$, we consider the semigroup $T(X, \mathcal{P}) = \{f\in \mathcal{T}_X\;|\; \forall…

Let L be a positive line bundle over a projective complex manifold X. Consider the space of holomorphic sections of the tensor power of order p of L. The determinant of a basis of this space, together with some given probability measure on…

For any numerical semigroup $S$, there are infinitely many numerical symmetric semigroups $T$ such that $S=\frac{T}{2}$ is their half. We are studying the Betti numbers of the numerical semigroup ring $K[T]$ when $S$ is a 3-generated…

Let F be a family of subsets of {1,2,...,n}. The width-degree of an element x in at least one member of F is the width of the family {U in F | x in U}. If F has maximum width-degree at most k, then F is locally k-wide. Bounds on the size of…

Suppose that $X$ be a nonempty set. Denote by $\mathcal{T}(X)$ the full transformation semigroup on $X$. For $\varnothing \neq Z\subseteq Y\subseteq X$, let $\mathcal{T}(X,Y,Z)=\{\alpha \in \mathcal{T}(X): Y\alpha \subseteq Z \}$. Then…

This paper is a survey, with few proofs, of ideas and notions related to self-similarity of groups, semi-groups and their actions. It attempts to relate these concepts to more familiar ones, such as fractals, self-similar sets, and…

It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…

We consider the subalgebra $\Delta$ in the group algebra of the symmetric group $G=S_{n_1+\dots+n_\nu}$ consisting of all functions invariant with respect to left and right shifts by elements of the Young subgroup $H:=S_{n_1}\times \dots…

We consider the relative configurational entropy per cell S_Delta as a measure of the degree of spatial disorder for systems of finite-sized objects. It is highly sensitive to deviations from the most spatially ordered reference…

Let $\Gamma $ be an infinite discrete group and $\mathsf{A}\subset \Gamma $ a nonempty finite subset. The set of permutations $\sigma $ of $\Gamma $ such that $s^{-1}\sigma (s)\in \mathsf{A}$ for every $s\in \Gamma $ can be identified with…

We characterize numerical semigroups $S$ with embedding dimension three attaining equality in the inequality $\max\Delta(S)+2\leq \operatorname{cat}(S)$, where $\Delta(S)$ denotes the Delta set of $S$ and $\operatorname{cat}(S)$ denotes the…

Let the map $f:[-1,1]\to[-1,1]$ have a.c.i.m. $\rho$ (absolutely continuous $f$-invariant measure with respect to Lebesgue). Let $\delta\rho$ be the change of $\rho$ corresponding to a perturbation $X=\delta f\circ f^{-1}$ of $f$. Formally…

Let H be the discrete 3-dimensional Heisenberg group with the standard generators x, y, z. The element Delta of the group algebra for H of the form Delta= (x+x^{-1}+y+y^{-1})/4 is called the Laplace operator. This operator can also be…