Related papers: The synchronisation hierarchy via coherent configu…

In this paper, we investigate structural properties of finite groups that are detected by certain group invariants arising from Dijkgraaf--Witten theory, a topological quantum field theory, in one space and one time dimension. In this…

We generalise the standard constructions of a Cayley graph in terms of a group presentation by allowing some vertices to obey different relators than others. The resulting notion of presentation allows us to represent every vertex…

We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…

In this paper, we theoretically and experimentally analyze sequential processors with limited communication between parts. We compare the expressivity of sequential quantum and classical processors under the same constraints. They consist…

Spectral properties of many finite convolution integral operators have been understood by finding differential operators that commute with them. In this paper we compile a complete list of such commuting pairs, extending previous work to…

The intention of the paper is to move a step towards a classification of network topologies that exhibit periodic quantum dynamics. We show that the evolution of a quantum system, whose hamiltonian is identical to the adjacency matrix of a…

This work introduces a new class of symmetric matrix structures, called harmonic structures, which enable the generation of all possible directed transitions $(x_i, x_{i+1})$ over a set of $n$ symbols, without internal repetitions. Unlike…

It is observed that the conjugacy growth series of the infinite fini-tary symmetric group with respect to the generating set of transpositions is the generating series of the partition function. Other conjugacy growth series are computed,…

Synchronization in networks of coupled oscillators is known to be largely determined by the spectral and symmetry properties of the interaction network. Here we leverage this relation to study a class of networks for which the threshold…

We prove that coherent configurations can be represented as modules over Frobenius structures in the category of real nonnegative matrices. We generalize the notion of admissible morphism from association schemes to coherent configurations.…

We study permutation groups of given minimal degree without the classical primitivity assumption. We provide sharp upper bounds on the order of a permutation group of minimal degree m and on the number of its elements of any given support.…

Quantum mechanics exhibits a wide range of nonclassical features, of which entanglement in multipartite systems takes a central place. In several specific settings, it is well known that nonclassicality (e.g., squeezing, spin squeezing,…

Li et al. in [Inf. Process. Lett. 77 (2001) 35--41] proposed the shuffle cube $SQ_{n}$ as an attractive interconnection network topology for massive parallel and distributed systems. By far, symmetric properties of the shuffle cube remains…

We introduce a combinatorial characterization of simpliciality for arrangements of hyperplanes. We then give a sharp upper bound for the number of hyperplanes of such an arrangement in the projective plane over a finite field, and present…

We introduce a notion of permutation presentations of modules over finite groups, and completely determine finite groups over which every module has a permutation presentation. To get this result, we prove that every coflasque module over a…

This paper concerns the general problem of classifying the finite deterministic automata that admit a synchronizing (or reset) word. (For our purposes it is irrelevant if the automata has initial or final states.) Our departure point is the…

Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relationship and introduce a universal construction of infinite…

Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…

To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…

For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group,…