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

We prove a broad generalization of a theorem of W. Burnside on real characters using permutation characters. Under a necessary hypothesis, We can give some control on multiplicities (a result that needs the Classification of Finite Simple…

We prove the complete intersection theorem and complete nontrivial-intersection theorem for systems of set partitions

Permutation clones generalise permutation groups and clone theory. We investigate permutation clones defined by relations, or equivalently, the automorphism groups of powers of relations. We find many structural results on the lattice of…

We study the Universality and Membership Problems for gate sets consisting of a finite number of quantum gates. Our approach relies on the techniques from compact Lie groups theory. We also introduce an auxiliary problem called Subgroup…

We study the structure of the absolute differential Galois group of a rational function field over an algebraically closed field of characteristic zero. In particular, we relate the behavior of differential embedding problems to the…

In this work, we prove that the permutation group of a Reed-Solomon code is given by the polynomials of degree one that leave the set of evaluation points invariant. Our results provide a straightforward proof of the well-known cases of the…

The goal of this paper is threefold. First, we describe the notion of dissociation for closed subgroups of the group of permutations on a countably infinite set and explain its numerous consequences on unitary representations…

We consider pairs of finitely presented, residually finite groups $P\hookrightarrow\G$ for which the induced map of profinite completions $\hat P\to \hat\G$ is an isomorphism. We prove that there is no algorithm that, given an arbitrary…

We continue the study of permutations of a finite regular semigroup that map each element to one of its inverses, providing a complete description in the case of semigroups whose idempotent generated subsemigroup is a union of groups. We…

This paper introduces quantum analogues of non-interactive perfect and statistical zero-knowledge proof systems. Similar to the classical cases, it is shown that sharing randomness or entanglement is necessary for non-trivial protocols of…

We classify the finite quasisimple groups whose commuting graph is perfect and we give a general structure theorem for finite groups whose commuting graph is perfect.

We prove that deciding whether a given input word contains as subsequence every possible permutation of integers $\{1,2,\ldots,n\}$ is coNP-complete. The coNP-completeness holds even when given the guarantee that the input word contains as…

We prove that the problems of deciding whether a quadratic equation over a free group has a solution is NP-complete.

We consider the polynomial Ideal Membership Problem (IMP) for ideals encoding combinatorial problems that are instances of CSPs over a finite language. In this paper, the input polynomial $f$ has degree at most $d=O(1)$ (we call this…

Let $M$ be a compact surface with boundary. We are interested in the question of how a group action on $M$ permutes a finite invariant set $X \subset int(M)$. More precisely, how the algebraic properties of the induced group of permutations…

We prove completeness for the main examples of infinite-dimensional Lie groups and some related topological groups.

We consider the permutation group algebra defined by Cameron and show that if the permutation group has no finite orbits, then no homogeneous element of degree one is a zero-divisor of the algebra. We proceed to make a conjecture which…

A set of $N$ permutations of $\{1,2,\dots,v\}$ is $(N,v,t)$-suitable if each symbol precedes each subset of $t-1$ others in at least one permutation. The central problems are to determine the smallest $N$ for which such a set exists for…

We prove that, up to adding a complement, every modular representation of a finite group admits a finite resolution by permutation modules.

We prove that every finite semigroup embeds in a finitely presented congruence-free monoid, and pose some questions around the Boone-Higman Conjecture.