18 citations · 28 across the 25 of their papers we have counts for
29 papers
On Word Representations and Embeddings in Complex Matrices
Paul C. Bell, George Kenison, Reino Niskanen +2
Embeddings of word structures into matrix semigroups provide a natural bridge between combinatorics on words and linear algebra. However, low-dimensional matrix semigroups impose s…
On the Identity and Group Problems for Complex Heisenberg Matrices
Paul C. Bell, Reino Niskanen, Igor Potapov +1
We study the Identity Problem, the problem of determining if a finitely generated semigroup of matrices contains the identity matrix; see Problem 3 (Chapter 10.3) in ``Unsolved Pro…
A Geometric Approach to Passive Localisation
Theofilos Triommatis, Igor Potapov, Gareth Rees +1
In this paper, we present a geometric framework for the passive localisation of static emitters. The objective is to localise the position of the emitters in a given area by centra…
Distributed Transformations of Hamiltonian Shapes based on Line Moves
Abdullah Almethen, Othon Michail, Igor Potapov
We consider a discrete system of simple indistinguishable devices, called \emph{agents}, forming a \emph{connected} shape on a two-dimensional square grid. Agents are equ…
Centralised Connectivity-Preserving Transformations for Programmable Matter: A Minimal Seed Approach
Matthew Connor, Othon Michail, Igor Potapov
We study a model of programmable matter systems consisting of devices lying on a 2-dimensional square grid which are able to perform the minimal mechanical operation of rotatin…
Combinatorial Algorithms for Multidimensional Necklaces
Duncan Adamson, Argyrios Deligkas, Vladimir V. Gusev +1
A necklace is an equivalence class of words of length over an alphabet under the cyclic shift (rotation) operation. As a classical object, there have been many algorithmic resu…