Related papers: Subgroup Chains and Lagrange Coordinatizations of …
In recent years, attempts to generalize lattice gauge theories to model topological order have been carried out through the so called $2$-gauge theories. These have opened the door to interesting new models and new topological phases which…
We determine explicit generators for a cohomology group constructed from a solution of a fuchsian linear differential equation and describe its relation with cohomology groups with coefficients in a local system. In the parameterized case,…
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…
Decomposition is a common tool for synthesis of many physical systems. It is also used for analyzing large scale systems which then known as tearing and reconstruction. On the other hand, commutativity of cascade connected systems have…
A geometric global formulation of the higher-order Lagrangian formalism for systems with finite number of degrees of freedom is provided. The formalism is applied to the study of systems with groups of Noetherian symmetries.
Let $T_X$ be the full transformation monoid over a finite set $X$, and fix some $a\in T_X$ of rank $r$. The variant $T_X^a$ has underlying set $T_X$, and operation $f\star g=fag$. We study the congruences of the subsemigroup $P=Reg(T_X^a)$…
A classic problem in enumerative combinatorics is to count the number of derangements, that is, permutations with no fixed point. Inspired by a recent generalization to facet derangements of the hypercube by Gordon and McMahon, we…
We prove that every finite dimensional representation of a finite group over a field of characteristic p admits a finite resolution by p-permutation modules. The proof involves a reformulation in terms of derived categories.
In this paper, we survey some of the recent advances on embeddings into finitely generated (left-orderable) simple group such that the overgroup preserves algorithmic, geometric, or algebraic information about the embedded group. We discuss…
Permutation polynomials over finite fields have important applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, etc. In this paper, we construct several new classes of permutation…
This is a report on our long term project to find an algorithm to decide if a finitely presented group has a non-trivial action on a tree.
We propose some new method of constructing configurations, which consists in consecutive inscribing copies of one underlying configuration. A uniform characterization of the obtained class and the one introduced in our paper untitled…
In the paper it is proven that Carter subgroups of a finite group are conjugate. A complete classification of Carter subgroups in finite almost simple groups is also obtained.
An efficient scheme to compute the geometric entanglement per lattice site for quantum many-body systems on a periodic finite-size chain is proposed in the context of a tensor network algorithm based on the matrix product state…
Finite symmetries abound in particle physics, from the weak doublets and generation triplets to the baryon octet and many others. These are usually studied by starting from a Lie group, and breaking the symmetry by choosing a particular…
Leptoquarks are theoretically well-motivated and have received increasing attention in recent years as they can explain several hints for physics beyond the Standard Model. In this article, we calculate the renormalisation group evolution…
Finite Lorentz groups acting on 4-dimensional vector spaces coordinatized by finite fields with a prime number of elements are represented as homomorphic images of countable, rational subgroups of the Lorentz group acting on real…
We introduce a new graph invariant of finite groups that provides a complete characterization of the splitting types of unramified prime ideals in normal number field extensions entirely in terms of the Galois group. In particular, each…
Let $G$ be a commutative algebraic group embedded in projective space and $\Gamma$ a finitely generated subgroup of $G$. From these data we construct a chain of algebraic subgroups of $G$ which is intimately related to obstructions to…
Structure monoids and groups are algebraic invariants of equational varieties. We show how to construct presentations of these objects from coherent categorifications of equational varieties, generalising several results of Dehornoy. We…