Related papers: Forcing among exact patterns of triods
We study exact module categories over the representation categories of finite-dimensional quasi-Hopf algebras. As a consequence we classify exact module categories over some families of pointed tensor categories with cyclic group of…
We present a class of mappings between models with topological mass mechanism and purely topological models in arbitrary dimensions. These mappings are established by directly mapping the fields of one model in terms of the fields of the…
Let $\mathcal{A}$ be an additive category and let $T\colon \mathcal{A}\rightarrow \mathcal{A}$ be an additive functor equipped with a natural transformation $\omega\colon \mathrm{Id}_{\mathcal{A}}\rightarrow T$. We prove that the homotopy…
A powerful way to study groups is via their actions on suitable spaces. Classifying spaces for families of subgroups are a type of these spaces, obtained by imposing some strict conditions on the fixed-point sets. We show how in the…
In this note we study the entropy spectrum of rotation classes for collections of finitely many continuous potentials $\varphi_1,\dots,\varphi_m:X\to \mathbb{R}$ with respect to the set of invariant measures of an underlying dynamical…
A new hierarchy of "exact" unification types is introduced, motivated by the study of admissibility for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by…
We formulate the notion of \emph{typical boundedness} of torsion on a family of abelian varieties defined over number fields. This means that the torsion subgroups of elements in the family can be made uniformly bounded by removing from the…
A \emph{binary tanglegram} is a drawing of a pair of rooted binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example, in phylogenetics, it is essential…
The $3x+1$ problem concerns the iteration of the map $T:\mathbb{Z}\to\mathbb{Z}$ defined by $T(x)=x/2$ for even $x$ and $T(x)=(3x+1)/2$ for odd $x$. We study the \emph{coefficient stopping time} dynamics of $T$ (in the sense of Terras) by…
The purpose of this article is to give a complete and general answer to the recurrent problem in continuum mechanics of the determination of the number and the type of symmetry classes of an even-order tensor space. This kind of…
In this paper, we introduce a particular class of matrices. We study the concept of a matrix to be \emph{balanced}. We study some properties of this concept in the context of matrix operations. We examine the behaviour of various matrix…
Multi-frequency forcing of systems undergoing a Hopf bifurcation to spatially homogeneous oscillations is investigated using a complex Ginzburg-Landau equation that systematically captures weak forcing functions that simultaneously hit the…
We show that for fixed $d>3$ and $n$ growing to infinity there are at least $(n!)^{d-2 \pm o(1)}$ different labeled combinatorial types of $d$-polytopes with $n$ vertices. This is about the square of the previous best lower bounds. As an…
We introduce a new class of structured symmetric matrices by extending the notion of perfect elimination ordering from graphs to weighted graphs or matrices. This offers a common framework capturing common vertex elimination orderings of…
We introduce and study the {\em orderly spanning trees} of plane graphs. This algorithmic tool generalizes {\em canonical orderings}, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning…
This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…
Exact sequences are a well known notion in homological algebra. We investigate here the more vague properties of 'homotopical exactness', appearing for instance in the fibre or cofibre sequence of a map. Such notions of exactness can be…
In this work, we relate the three main formalisms for the notion of pasting diagram in strict $\omega$-categories: Street's parity complexes, Johnson's pasting schemes and Steiner's augmented directed complexes. In the process, we show that…
In this paper, based on results of exact learning, test theory, and rough set theory, we study arbitrary infinite families of concepts each of which consists of an infinite set of elements and an infinite set of subsets of this set called…
In this expository article, we describe the recent approach, motivated by ergodic theory, towards detecting arithmetic patterns in the primes, and in particular establishing that the primes contain arbitrarily long arithmetic progressions.…