Zobrazeno 1 - 10
of 39
pro vyhledávání: '"Dong, Ruiwen"'
We survey solvability of equations in wreath products of groups, and prove that the quadratic diophantine problem is solvable in wreath products of Abelian groups. We consider the related question of determining commutator width, and prove that the q
Externí odkaz:
http://arxiv.org/abs/2410.04905
Autor:
Dong, Ruiwen
We show that Submonoid Membership is decidable in n-dimensional lamplighter groups $(\mathbb{Z}/p\mathbb{Z}) \wr \mathbb{Z}^n$ for any prime $p$ and integer $n$. More generally, we show decidability of Submonoid Membership in semidirect products of t
Externí odkaz:
http://arxiv.org/abs/2409.07077
Autor:
Dong, Ruiwen
We show that it is undecidable whether a system of linear equations over the Laurent polynomial ring $\mathbb{Z}[X^{\pm}]$ admit solutions where a specified subset of variables take value in the set of monomials $\{X^z \mid z \in \mathbb{Z}\}$. In pa
Externí odkaz:
http://arxiv.org/abs/2406.08480
Autor:
Bodart, Corentin, Dong, Ruiwen
The Tits alternative states that a finitely generated matrix group either contains a nonabelian free subgroup $F_2$, or it is virtually solvable. This paper considers two decision problems in virtually solvable matrix groups: the Identity Problem (do
Externí odkaz:
http://arxiv.org/abs/2404.02264
Autor:
Dong, Ruiwen
In this article we survey recent progress in the algorithmic theory of matrix semigroups. The main objective in this area of study is to construct algorithms that decide various properties of finitely generated subsemigroups of an infinite group $G$,
Externí odkaz:
http://arxiv.org/abs/2309.10943
Autor:
Dong, Ruiwen
We consider two decision problems in infinite groups. The first problem is Subgroup Intersection: given two finitely generated subgroups $\langle \mathcal{G} \rangle, \langle \mathcal{H} \rangle$ of a group $G$, decide whether the intersection $\lang
Externí odkaz:
http://arxiv.org/abs/2309.08811
Autor:
Dong, Ruiwen
We consider semigroup algorithmic problems in finitely generated metabelian groups. Our paper focuses on three decision problems introduced by Choffrut and Karhum\"{a}ki (2005): the Identity Problem (does a semigroup contain a neutral element?), the
Externí odkaz:
http://arxiv.org/abs/2304.12893
Autor:
Dong, Ruiwen
We consider semigroup algorithmic problems in the wreath product $\mathbb{Z} \wr \mathbb{Z}$. Our paper focuses on two decision problems introduced by Choffrut and Karhum\"{a}ki (2005): the Identity Problem (does a semigroup contain the neutral eleme
Externí odkaz:
http://arxiv.org/abs/2302.05939
Autor:
Dong, Ruiwen
We consider the following problem: given $d \times d$ rational matrices $A_1, \ldots, A_k$ and a polyhedral cone $\mathcal{C} \subset \mathbb{R}^d$, decide whether there exists a non-zero vector whose orbit under multiplication by $A_1, \ldots, A_k$
Externí odkaz:
http://arxiv.org/abs/2302.01003
Autor:
Dong, Ruiwen
We consider semigroup algorithmic problems in the Special Affine group $\mathsf{SA}(2, \mathbb{Z}) = \mathbb{Z}^2 \rtimes \mathsf{SL}(2, \mathbb{Z})$, which is the group of affine transformations of the lattice $\mathbb{Z}^2$ that preserve orientatio
Externí odkaz:
http://arxiv.org/abs/2301.09502