We introduce a new strategy in solving the truncated complex moment problem. To this aim we investigate recursive doubly indexed sequences and their characteristic polynomials. A characterization of recursive doubly indexed moment... more
We present a simple visual description of the topology of the space of three-dimensional rotations, requiring just intuition, imagination and no advanced math.
We show that there is a distortion element in a finitely generated subgroup G of the automorphism group of the full shift, namely an element of infinite order whose word norm grows polylogarithmically. As a corollary, we obtain a lower... more
To each one-dimensional subshift X, we may associate a winning shift W(X) which arises from a combinatorial game played on the language of X. Previously it has been studied what properties of X does W(X) inherit. For example, X and W(X)... more
We introduce a notion of "simulation" for labelled graphs, in which edges of the simulated graph are realized by regular expressions in the simulating graph, and prove that the tiling problem (aka "domino problem") for the simulating... more
We say that a finitely generated group Γ is (dynamically) self-simulable if every effectively closed action of Γ on a closed subset of {0, 1} N is the topological factor of a Γ-subshift of finite type. We show that self-simulable groups... more
The second author introduced with I. Törmä a two-player word-building game [Playing with Subshifts, Fund. Inform. 132 (2014), 131-152]. The game has a predetermined (possibly finite) choice sequence α 1 , α 2 , . . . of integers such that... more
In this short article, we study factor colorings of aperiodic linearly recurrent infinite words. We show that there always exists a coloring which does not admit a monochromatic factorization of the word into factors of increasing lengths.
We introduce a notion of "simulation" for labelled graphs, in which edges of the simulated graph are realized by regular expressions in the simulating graph, and prove that the tiling problem (aka "domino problem") for the simulating... more
We say that a finitely generated group Γ is (dynamically) self-simulable if every effectively closed action of Γ on a closed subset of {0, 1} N is the topological factor of a Γ-subshift of finite type. We show that self-simulable groups... more
We study qualitative properties of two-dimensional freezing cellular automata with a binary state set initialized on a random configuration. If the automaton is also monotone, the setting is equivalent to bootstrap percolation. We explore... more
To each one-dimensional subshift X, we may associate a winning shift W(X) which arises from a combinatorial game played on the language of X. Previously it has been studied what properties of X does W(X) inherit. For example, X and W(X)... more
We give some optimal size generating sets for the group generated by shifts and local permutations on the binary full shift. We show that a single generator, namely the fully asynchronous application of the elementary cellular automaton... more
The second author introduced with I. Törmä a two-player word-building game [Fund. Inform. 132 (2014) 131–152]. The game has a predetermined (possibly finite) choice sequence α1, α2, … of integers such that on round n the player A chooses... more
We study the message size complexity of recognizing, under the broadcast congested clique model, whether a fixed graph H appears in a given graph G as a minor, as a subgraph or as an induced subgraph. The n nodes of the input graph G are... more
In this article, we study countable sofic shifts of Cantor-Bendixson rank at most 2. We prove that their conjugacy problem is complete for GI, the complexity class of graph isomorphism, and that the existence problems of block maps,... more
In this article, we prove that for all pairs of primitive Pisot or uniform substitutions with the same dominating eigenvalue, there exists a finite set of block maps such that every block map between the corresponding subshifts is an... more
For simple graphs G and H, their size Ramsey number r(G, H) is the smallest possible size of F such that for any red-blue coloring of its edges, F contains either a red G or a blue H. Similarly, we can define the connected size Ramsey... more
Let F , G and H be simple graphs. The size Ramsey number r(G, H) of G and H is the smallest possible size of F such that for any red-blue coloring of its edges, F contains either a red G or a blue H. Similarly, we can define the connected... more
Let G=(V,E) be a simple graph. A vertex labeling f:V(G)→{1,2,⋯,k} is defined to be a local inclusive (respectively, non-inclusive) d-distance vertex irregular labeling of a graph G if for any two adjacent vertices x,y∈V(G) their weights... more
In this paper we develop several general methods for analysing flag-transitive pointimprimitive 2-designs, which give restrictions on both the automorphisms and parameters of such designs. These constitute a tool-kit for analysing these... more
We give a unified approach to analysing, for each positive integer s, a class of finite connected graphs that contains all the distance transitive graphs as well as the locally s-arc transitive graphs of diameter at least s. A graph is in... more
Twisted permutation codes, introduced recently by the second and third authors, are frequency permutation arrays. They are similar to repetition permutation codes, in that they are obtained by a repetition construction applied to a... more
Delandtsheer and Doyen bounded, in terms of the block size, the number of points of a point-imprimitive, block-transitive 2-design. To do this they introduced two integer parameters m, n, now called Delandtsheer-Doyen parameters, linking... more
In 1987, Huw Davies proved that, for a flag-transitive point-imprimitive 2-(v, k, λ) design, both the block-size k and the number v of points are bounded by functions of λ, but he did not make these bounds explicit. In this paper we... more
A graph is Cartesian decomposable if it is isomorphic to a Cartesian product of (more than one) strictly smaller graphs, each of which has more than one vertex and admits no such decomposition. These smaller graphs are called the... more
The Johnson graph J(v, k) has, as vertices, the k-subsets of a v-set V and as edges the pairs of k-subsets with intersection of size k -1. We introduce the notion of a neighbour-transitive code in J(v, k). This is a vertex subset Γ such... more
The automorphism group of a flag-transitive 6-(v, k, 2) design is a 3-homogeneous permutation group. Therefore, using the classification theorem of 3-homogeneous permutation groups, the classification of flag-transitive 6-(v, k,2) designs... more
We consider a code to be a subset of the vertex set of a Hamming graph. We examine elusive pairs, code-group pairs where the code is not determined by knowledge of its set of neighbours. We construct a new infinite family of elusive... more
We give a construction of a family of designs with a specified pointpartition, and determine the subgroup of automorphisms leaving invariant the point-partition. We give necessary and sufficient conditions for a design in the family to... more
We investigate locally n×n grid graphs, that is, graphs in which the neighbourhood of any vertex is the Cartesian product of two complete graphs on n vertices. We consider the subclass of these graphs for which each pair of vertices at... more
We discuss recent progress on the problem of classifying point-primitive generalised polygons. In the case of generalised hexagons and generalised octagons, this has reduced the problem to primitive actions of almost simple groups of Lie... more
In this paper we develop several general methods for analysing flag-transitive point-imprimitive 2-designs, which give restrictions on both the automorphisms and parameters of such designs. These constitute a tool-kit for analysing these... more
The mathematics of shuffling a deck of 2n cards with two "perfect shuffles" was brought into clarity by Diaconis, Graham and Kantor. Here we consider a generalisation of this problem, with a so-called "many handed dealer" shuffling kn... more
A graph Γ is said to be locally primitive if, for each vertex α, the stabilizer in Aut Γ of α induces a primitive permutation group on the set of vertices adjacent to α. In 1978, Richard Weiss conjectured that for a finite... more
In this paper we complete a classification of finite linear spaces S with line size at most 12 admitting a line-transitive point-imprimitive subgroup of automorphisms. The examples are the Desarguesian projective planes of orders 4, 7, 9... more
An approach to analysing the family of Cayley graphs for a finite group G is given which identifies normal edge-transitive Cayley graphs as a sub-family of central importance. These are the Cayley graphs for G for which a subgroup of... more
Let r be finite connected and G a group of automorphisms of r which is transitive on vertices. Suppose that, for a vertex 0 of r, S ~ G~(O') ::; Aut S for some simple group S with S acting primitively on the set r( a) of neighbours of 0,... more
We consider a code to be a subset of the vertex set of a Hamming graph. The set of s-neighbours of a code is the set of vertices, not in the code, at distance s from some codeword, but not distance less than s from any codeword. A... more
A two-row array of integers \[ \alpha_{n}= \begin{pmatrix}a_1 & a_2 & \cdots & a_n\\ b_1 & b_2 & \cdots & b_n \end{pmatrix} \] is said to be in lexicographic order if its columns are in lexicographic order (where character significance... more
This study discusses the Fuzzy Elimination Et Choix Traduisant La Realite (ELECTRE) method that can be applied to make a decision support. This method was chosen because it is one of the methods used to rank and determine the best... more
A decomposition of graph G is collection of subgraphs 〖{H_i}〗_(i=1)^n from G such that H_i [E_i] for E_i is a subset of E(G) and 〖{E_i}〗_(i=1)^n is a partition of E(G). The purpose of the research was to determine the decomposition of the... more
Penelitian ini menjelaskan bahwa graf multi star dan graf hairy cycle adalah super sisi ajaib. Masalah pelabelan dalam teori graf mulai dikembangkan pada pertengahan tahun 1960-an. Pelabelan pada suatu graf muncul pertama kali dari karya... more
Upper bounds on the maximum number of minimal codewords in a binary code follow from the theory of matroids. Random coding provide lower bounds. In this paper we compare these bounds with analogous bounds for the cycle code of graphs.... more
A matrix A ∈ Mn(R) with coefficients in any ring R is a quasipermutation matrix if each row and each column has at most one nonzero element. It is shown that a singular quasi-permutation matrix with coefficients in a domain is a product... more