相关论文: The Hurwitz Equivalence Problem is Undecidable

Irreducible trinomials of given degree n over $F_2$ do not always exist and in the cases that there is no irreducible trinomial of degree n it may be effective to use trinomials with an irreducible factor of degree n. In this paper we…

The decidability of the reachability problem for finitary PCF has been used as a theoretical basis for fully automated verification tools for functional programs. The reachability problem, however, often becomes undecidable for a slight…

In this paper we give an algorithm for solving a main case of the conjugacy problem in the braid groups. We also prove that half-twists satisfy a special root property which allows us to reduce the solution for the conjugacy problem in…

Every matrix polynomial $\mathbf{f}_n$ can be written in the form \[ \mathbf{f}_n(z)=\mathbf{h}(z^2)+z\,\mathbf{g}_n(z^2). \] The matrix polynomial $\mathbf{f}_{2m}$ is said to be of Hurwitz type if the expression…

The satisfiability problem for SPARQL patterns is undecidable in general, since the expressive power of SPARQL 1.0 is comparable with that of the relational algebra. The goal of this paper is to delineate the boundary of decidability of…

We consider two applications of the strata of differentials of the second kind (all residues equal to zero) with fixed multiplicities of zeros and poles: Positivity: In genus $g=0$ we show any associated divisorial projection to…

We consider the two-variable fragment FO^2[<] of first-order logic over finite words. Numerous characterizations of this class are known. Th\'erien and Wilke have shown that it is decidable whether a given regular language is definable in…

We prove the irreducibility of the space parametrizing branched covers of a fixed Riemann surface $B$ of degree $d$, with at least 2d branch points, and with monodromy group equal to $S_d$. The result is classical for $g(B)=0$. The result…

With each holomorphic map $f: R \rightarrow \mathbb C\mathbb P^1$, where $R$ is a compact Riemann surface, one can associate a combinatorial datum consisting of the genus $g$ of $R$, the degree $n$ of $f$, the number $q$ of branching points…

We introduce and study a semigroup structure on the set of irreducible components of the Hurwitz space of marked coverings of a complex projective curve with given Galois group of the coverings and fixed ramification type. As application,…

In this article, we study the irreducibility of representations of the singular braid group on $n$ strands, namely $SB_n$. Our first finding is the determination of the forms of all irreducible representations $\rho : SB_2 \to…

We prove the irreducibility of the Hurwitz spaces which parametrize Galois coverings of P^1 whose Galois group is an arbitrary Weyl group and the local monodromies are reflections. This generalizes a classical theorem due to Clebsch and…

The Hurwitz problem asks which ramification data are realizable, that is appear as the ramification type of a covering. We use dessins d'enfant to show that families of genus 1 regular ramification data with small changes are realizable…

Dependent Object Types (DOT) is a calculus with path dependent types, intersection types, and object self-references, which serves as the core calculus of Scala 3. Although the calculus has been proven sound, it remains open whether type…

In the 60's, Berger famously showed that translational tilings of $\mathbb{Z}^2$ with multiple tiles are algorithmically undecidable. Recently, Bhattacharya proved the decidability of translational monotilings (tilings by translations of a…

We settle the problem of the uniqueness of normalized homeomorphic solutions to nonlinear Beltrami equations $\bar\partial f(z)=H(z, \partial f(z))$. It turns out that the uniqueness holds under definite and explicit bounds on the…

We prove that Knapsack problem (KP) is undecidable for any group of nilpotency class two if the number of generators (without torsion) of the derived subgroup is at least 322. This result together with the fact that if KP is undecidable for…

Hurwitz numbers enumerate ramified coverings of the Riemann sphere with fixed ramification data. Certain kinds of ramification data are of particular interest, such as double Hurwitz numbers, which count covers with fixed arbitrary…

Recently it was shown that it is undecidable whether a term rewrite system can be proved terminating by a polynomial interpretation in the natural numbers. In this paper we show that this is also the case when restricting the…

Many results in extremal graph theory can be formulated as certain polynomial inequalities in graph homomorphism densities. Answering fundamental questions raised by Lov{\'a}sz, Szegedy and Razborov, Hatami and Norine proved that…