Related papers: Dense Chains, Antichains, and Universal Partial Or…

In this paper we focus on modules over a finite chain ring $\mathcal{R}$ of size $q^s$. We compute the density of free modules of $\mathcal{R}^n$, where we separately treat the asymptotics in $n,q$ and $s$. In particular, we focus on two…

For the partition graph $G_n$, whose vertices are the partitions of $n$ and whose edges correspond to elementary unit transfers between parts, we develop a degree theory with three levels: exact value theory, exact profile theory, and…

One-weight codes, in which all nonzero codewords share the same weight, form a highly structured class of linear codes with deep connections to finite geometry. While their classification is well understood in the Hamming and rank metrics -…

Separations among the first order logic ${\cal R}ing(0,+,*)$ of finite residue class rings, its extensions with generalized quantifiers, and in the presence of a built-in order are shown, using algebraic methods from class field theory.…

Brauer and Thrall conjectured that a finite-dimensional algebra over a field of bounded representation type is actually of finite representation type and a finite-dimensional algebra (over an infinite field) of infinite representation type…

Set Shaping Theory (SST) moves beyond the classical fixed-space model by constructing bijective mappings the original sequence set into structured regions of a larger sequence space. These shaped subsets are characterized by a reduced…

We consider various collections of functions from the Baire space X into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings,…

First-order logic has been established as an important tool for modeling and verifying intricate systems such as distributed protocols and concurrent systems. These systems are parametric in the number of nodes in the network or the number…

Stochastic blockmodels are generative network models where the vertices are separated into discrete groups, and the probability of an edge existing between two vertices is determined solely by their group membership. In this paper, we…

An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…

This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…

Let $X$ be a Polish space and $K$ a separable compact subset of the first Baire class on $X$. For every sequence $\bs$ dense in $\kk$, the descriptive set-theoretic properties of the set \[ \lbf=\{L\in[\nn]: (f_n)_{n\in L} \text{is…

It has been known for almost 200 years that some angles cannot be trisected by straightedge and compass alone. This paper studies the set of such angles as well as its complement $\mathcal{T}$, both regarded as subsets of the unit circle…

We first show that infinite satisfiability can be reduced to finite satisfiability for all prenex formulas of Separation Logic with $k\geq1$ selector fields ($\seplogk{k}$). Second, we show that this entails the decidability of the finite…

The sequence space of all real-valued sequences, denoted $Seq(\mathbb{R})$, is typically investigated through the lens of infinite-dimensional vector spaces, utilizing Banach space norms or Schauder bases. This work proposes a…

Our contribution is a bounded cubic compilation theorem. For each fixed resource parameter $k$, syntactic proof checking at resource level $k$ is faithfully represented by a finite bounded-domain system of cubic polynomial equations. Every…

We prove that pointwise finite-dimensional S^1 persistence modules over an arbitrary field decompose uniquely, up to isomorphism, into the direct sum of a bar code and finitely-many Jordan cells. These persistence modules have also been…

We define a new category of non-archimedean analytic spaces over a complete discretely valued field, which we call uniformly rigid. It extends the category of rigid spaces, and it can be described in terms of bounded functions on products…

We study `definable' subsets of Baire space $\mathcal{N}$. The logic of our arguments is intuitionistic and we use L.E.J.~Brouwer's Thesis on bars in $\mathcal{N}$ and his continuity axioms. We avoid the operation of taking the complement…

In a recursive way and by including a parameter, we introduce a family of deterministic scale-free networks. The resulting networks exhibit small-world effects. We calculate the exact results for the degree exponent, the clustering…