Related papers: Nielsen Equivalence in Fuchsian groups

The classification, up to a center-affinity, of the homogeneous quadratic differential systems defined on $\mathbb{R}^{3}$ that have at least a semisimple derivation with one-dimensional kernel, is achieved. It is proved that there exist 35…

For numerical semigroups with a specified list of (not necessarily minimal) generators, we describe the asymptotic distribution of factorization lengths with respect to an arbitrary modulus. In particular, we prove that the factorization…

We classify combinatorial Dyson-Schwinger equations giving a Hopf subalgebra of the Hopf algebra of Feynman graphs of the considered Quantum Field Theory. We first treat single equations with an arbitrary number (eventually infinite) of…

After 100 years of effort, the classification of all the finite subgroups of SU(3) is yet incomplete. The most recently updated list can be found in P.O. Ludl, J. Phys. A: Math. Theor. 44 255204 (2011), where the structure of the series (C)…

In this paper we determine the irreducible projective representations of sporadic simple groups over an arbitrary algebraically closed field F, whose image contains an almost cyclic matrix of prime-power order. A matrix M is called cyclic…

Folding subgroups give a way to realize non-simply-laced Coxeter groups as subgroups of simply-laced Coxeter groups. In this paper, we study how folding subgroups of finite and affine type are distributed length-wise by calculating the…

The equivalence (or weak equivalence) classes of orientation-preserving free actions of a finite group G on an orientable 3-dimensional handlebody of genus g can be enumerated in terms of sets of generators of G. They correspond to the…

Given two maps f_1, f_2 : M^m \longrightarrow N^n between manifolds of the indicated arbitrary dimensions, when can they be deformed away from one another? More generally: what is the minimum number MCC (f_1, f_2) of pathcomponents of the…

We present a category equivalent to that of semi-Nelson algebras. The objects in this category are pairs consisting of a semi-Heyting algebra and one of its filters. The filters must contain all the dense elements of the semi-Heyting…

Let $G$ be a connected, reductive group over a non-archimedean local field $F$. Let $\breve F$ be the completion of the maximal unramified extension of $F$ contained in a separable closure $F_s$. In this article, we construct a Tits group…

We use a recent characterization of minimal value set polynomials and $q$- Frobenius nonclassical curves to construct curves that generalize the Hermitian curve. The genus $g$ and the number $N$ of $\mathbb{F}_q$-rational points of the…

The densities of small linear structures (such as arithmetic progressions) in subsets of Abelian groups can be expressed as certain analytic averages involving linear forms. Higher-order Fourier analysis examines such averages by…

We generalize some identities and q-identities previously known for the symmetric group to Coxeter groups of type B and D. The extended results include theorems of Foata and Sch\"utzenberger, Gessel, and Roselle on various distributions of…

The Andrews-Curtis conjecture asserts that, for a free group $F_n$ of rank $n$ and a free basis $(x_1,...,x_n)$, any normally generating tuple $(y_1,...,y_n)$ is Andrews-Curtis equivalent to $(x_1,...,x_n)$. This equivalence corresponds to…

We prove that the existence spectrum of Mendelsohn triple systems whose associated quasigroups satisfy distributivity corresponds to the Loeschian numbers, and provide some enumeration results. We do this by considering a description of the…

A generalized numerical semigroup is a submonoid of $\mathbb{N}^d$ with finite complement in it. In this work we study some properties of three different classes of generalized numerical semigroups. In particular, we prove that the first…

Starting from a Hopf algebra endowed with an action of a group G by Hopf automorphisms, we construct (by a twisted double method) a quasitriangular Hopf G-coalgebra. This method allows us to obtain non-trivial examples of quasitriangular…

We classify Haag-dual Poincar\'e covariant subsystems $\B\subset \F$ of a graded-local net $\F$ on 4D Minkowski spacetime which satisfies standard assumptions and has trivial superselection structure. The result applies to the canonical…

Composing with the inclusion $\mathsf{Set}\to\mathsf{Cat} $, a graph $G$ internal to $\mathsf{Set} $ becomes a graph of discrete categories, the coinserter of which is the category freely generated by $G$. Introducing a suitable definition…

We consider a Heegaard splitting M=H_1 \cup_S H_2 of a 3-manifold M having an essential disk D in H_1 and an essential surface F in H_2 with |D \cap F|=1. (We require that boundary of F is in S when H_2 is a compressionbody with non-empty…