Related papers: Bounded degree and planar spectra

We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…

For an essentially small triangulated category $\mathcal{T}$, we introduce the notion of prime thick subcategories and define the spectrum of $\mathcal{T}$, which shares the basic properties with the spectrum of a tensor triangulated…

The maximum number of vertices in a graph of maximum degree $\Delta\ge 3$ and fixed diameter $k\ge 2$ is upper bounded by $(1+o(1))(\Delta-1)^{k}$. If we restrict our graphs to certain classes, better upper bounds are known. For instance,…

In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…

When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…

We study the degree spectra and reverse-mathematical applications of computably enumerable and co-computably enumerable partial orders. We formulate versions of the chain/antichain principle and ascending/descending sequence principle for…

Let $E\supseteq F$ be a field extension and $M$ a graded Lie algebra of maximal class over $E$. We investigate the $F$-subalgebras $L$ of $M$, generated by elements of degree $1$. We provide conditions for $L$ being either ideally…

The genus spectrum of a finite group $G$ is a set of integers $g \geq 2$ such that $G$ acts on a closed orientable compact surface $\Sigma_g$ of genus $g$ preserving the orientation. In this paper we complete the study of spectrum sets of…

The degree of a projective subscheme has an upper bound in term of the codimension and the reduction number. If a projective variety has an almost maximal degree, that is, the degree equals to the upper bound minus one, then its Betti table…

We introduce the category of finite strings and study its basic properties. The category is closely related to the augmented simplex category, and it models categories of linear representations. Each lattice of non-crossing partitions…

A one-degree-of-freedom graph is a graph obtained from a minimally rigid graph in the plane and removing an edge. For such graph, the set of realisations with fixed edge length, modulo rotations and reflections, is an algebraic curve. The…

An upper dominating set in a graph is a minimal (with respect to set inclusion) dominating set of maximum cardinality. The problem of finding an upper dominating set is generally NP-hard. We study the complexity of this problem in classes…

We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.

For the algebra $A$ in the title, its prime, primitive and maximal spectra are classified. The group of automorphisms of $A$ is determined. The simple unfaithful $A$-modules and the simple weight $A$-modules are classified.

In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…

We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…

A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. A graph, together with a 1-planar drawing is called 1-plane. Brandenburg et al. showed that there are maximal 1-planar graphs with only…

The set A = {a_n} of nonnegative integers is an asymptotic basis of order h if every sufficiently large integer can be represented as the sum of h elements of A. If a_n ~ alpha n^h for some real number alpha > 0, then alpha is called an…

The problem of phase retrieval is a difficult one which remains far from solved. Two homometric sets are always connected by way of a convolution product by some spectral unit, though not necessarily in a unique way. Here we elucidate one…

For a sequence of random structures with $n$-element domains over a relational signature, we define its first order (FO) complexity as a certain subset in the Banach space $\ell^{\infty}/c_0$. The well-known FO zero-one law and FO…