Related papers: On the Double Coset Membership Problem for Permuta…

We consider the decision problem of whether a particular Gromov--Witten invariant on a partial flag variety is zero. We prove that for the $3$-pointed, genus zero invariants, this problem is in the complexity class ${\sf AM}$ assuming the…

The permutation representation afforded by a Coxeter group W acting on the cosets of a standard parabolic subgroup inherits many nice properties from W such as a shellable Bruhat order and a flat deformation over Z[q] to a representation of…

We investigate the complexity of deciding, given a multiplication table representing a semigroup S, a subset X of S and an element t of S, whether t can be expressed as a product of elements of X. It is well-known that this problem is…

Finite groups with given systems of permuteral and strongly permuteral subgroups are studied. New characterizations of w-supersoluble and supersoluble groups are received.

We consider the problem of deciding if a given three-party entangled pure state can be converted, with a non-zero success probability, into a given two-party pure state through local quantum operations and classical communication. We show…

In this paper we prove a finiteness result concerning the Chow group of zero-cycles for varieties over $p$-adic local fields. In this final version, there are several corrections concerning mathematical symbols and reference to related…

We indicate a natural generalization of the concept of subgroup commutativity degree of a finite group and a list of open problems on these new concepts.

Let $G$ be an infinite abelian group with $|2G|=|G|$. We show that if $G$ is not the direct sum of a group of exponent 3 and the group of order 2, then $G$ possesses a perfect additive basis; that is, there is a subset $S\subseteq G$ such…

Extending earlier work of Guralnick and of Cai and Zhang, we classify the almost simple groups which have transitive permutation representations of prime power degree $p^k$, and those which have $p$-complements (stabilisers of order coprime…

In this paper we show that the following problem is NP-complete: Given an alphabet $\Sigma$ and two strings over $\Sigma$, the question is whether there exists a permutation of $\Sigma$ which is a subsequence of both of the given strings.

We survey a research program on the strong convergence of unitary and permutation representations of discrete groups. We also take the opportunity to flesh out details that have not appeared elsewhere.

In this paper, some zeros and non-zeros in the character tables of symmetric groups are displayed in the partition forms. In particular, more zeros of self conjugate partitions beside odd permutations are heavily investigated.

In this paper, the Identity Problem for certain groups, which asks if the subsemigroup generated by a given finite set of elements contains the identity element, is related to problems regarding ordered groups. Notably, the Identity Problem…

We prove that the ideal membership problem and the subalgebra membership problem are algorithmically undecidable for differential polynomial algebras with at least two basic derivation operators.

We study intersection theoretic problems in the setting of Chow-Witt groups with coefficients in a fixed Milnor-Witt cycle algebra over a perfect field. We prove that the product maps on such groups satisfy the following property: given two…

We define the symmetric Post Correspondence Problem (PCP) and prove that it is undecidable. As an application we show that the original proof of undecidability of the freeness problem for 3-by-3 integer matrix semigroups works for the…

We prove a result on perfect cliques with respect to countably many G-delta relations on a complete metric space. As an application, we show that a Polish group contains a free subgroup generated by a perfect set as long as it contains any…

In this article we present an unpublished proof of W. Thurston that pure braid groups have the congruence subgroup property.

This paper proves that several interactive proof systems are zero-knowledge against quantum attacks. This includes a few well-known classical zero-knowledge proof systems as well as quantum interactive proof systems for the complexity class…

Consider a discrete valuation ring $R$ whose residue field is finite of cardinality at least $3$. For a finite torsion module, we consider transitive subsets $O$ under the action of the automorphism group of the module. We prove that the…