Related papers: A Factorization Theorem for Forest Algebras
We extend the left-to-right Lyndon factorisation of a word to the left Lyndon tree construction of a Lyndon word. It yields an algorithm to sort the prefixes of a Lyndon word according to the infinite ordering defined by Dolce et al.…
A general deformation theory of algebras which factorise into two subalgebras is studied. It is shown that the classification of deformations is related to the cohomology of a certain double complex reminiscent of the Gerstenhaber-Schack…
When digitizing a print bilingual dictionary, whether via optical character recognition or manual entry, it is inevitable that errors are introduced into the electronic version that is created. We investigate automating the process of…
Using a regularization by putting the system in finite volume, we develop a novel approach to form factor perturbation theory for nonintegrable models described as perturbations of integrable ones. This permits to go beyond first order in…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
In this paper we study some special classes of division algebras over a Laurent series field with arbitrary residue field. We call the algebras from these classes as splittable and good splittable division algebras. It is shown that these…
Sampling theory has traditionally drawn tools from functional and complex analysis. Past successes, such as the Shannon-Nyquist theorem and recent advances in frame theory, have relied heavily on the application of geometry and analysis.…
A new concept of meromorphic $\Sigma$-factorization, for H\"{o}lder continuous functions defined on a contour $\Gamma$ that is the pullback of $\dot{\mathbb{R}}$ (or the unit circle) in a Riemann surface $\Sigma$ of genus 1, is introduced…
Canonical distances such as Euclidean distance often fail to capture the appropriate relationships between items, subsequently leading to subpar inference and prediction. Many algorithms have been proposed for automated learning of suitable…
A sharp bound is obtained for the number of ways to express the monomial $X^n$ as a product of linear factors over $\mathbb{Z}/p^{\alpha}\mathbb{Z}$. The proof relies on an induction-on-scale procedure which is used to estimate the number…
The purpose of this paper is to build an algebraic framework suited to regularise branched structures emanating from rooted forests and which encodes the locality principle. This is achieved by means of the universal properties in the…
The precise formulation of derivation for tree-adjoining grammars has important ramifications for a wide variety of uses of the formalism, from syntactic analysis to semantic interpretation and statistical language modeling. We argue that…
In 2018, the concept of a fort in graph theory was introduced as a non-empty subset of vertices satisfying the condition that no vertex outside the set has exactly one neighbor in the set. Since then, forts have played a significant role in…
Decompositional theories describe the ways in which a global physical system can be split into subsystems, facilitating the study of how different possible partitions of a same system interplay, e.g. in terms of inclusions or signalling. In…
Branes and defects in topological Landau-Ginzburg models are described by matrix factorisations. We revisit the problem of deforming them and discuss various deformation methods as well as their relations. We have implemented these…
In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems,…
The grammar representation of a narrowing tree for a syntactically deterministic conditional term rewriting system and a pair of terms is a regular tree grammar that generates expressions for substitutions obtained by all possible…
Treewidth is a well-studied decompositional parameter to measure the tree-likeness of a graph. While the propositional satisfiability problem (SAT) is known to be tractable when parameterized by the treewidth of the underlying primal graph,…
An attractive mechanism to specify global constraints in rostering and other domains is via formal languages. For instance, the Regular and Grammar constraints specify constraints in terms of the languages accepted by an automaton and a…