Projects / Programmes
Algebraic and metric aspects of symmetry in combinatorial objects
Code |
Science |
Field |
Subfield |
1.01.05 |
Natural sciences and mathematics |
Mathematics |
Graph theory |
Code |
Science |
Field |
P110 |
Natural sciences and mathematics |
Mathematical logic, set theory, combinatories |
P120 |
Natural sciences and mathematics |
Number theory, field theory, algebraic geometry, algebra, group theory |
symmetry, mathematics, combinatorics, algebra, graph theory, group theory, permutation group, group action, transitive graph
Researchers (4)
Organisations (1)
Abstract
The research project will focus mainly on algebraic and metric aspects of symmetry in combinatorial objects. A wider frame of the proposed project is actions of groups on finite or infinite sets, graphs, geometries and other combinatorial objects, as well as the opposite, that is, a treatment of symmetry properties of given combinatorial objects and their formalisation through group theory. The project will consider, among other: normally imprimitive actions and graphs with normally imprimitive automorphism groups (the action of a group on a set is normally imprimitive if every partition of the set that is left invariant by the group action, consists of orbits of a normal subgroup in the initial group), different transitivities in graphs, such as adjacency-transitivity (a graph is adjacency-transitive if every its vertex can be mapped to another vertex through a sequence of adjacency-automorphisms of the graph, which are automorphisms sending each vertex to a neighbour or fixing it), half-arc-transitivity (a graph is half-arc-transitive if its automorphism group has a subgroup acting transitively on the set of vertices and on the set of edges of the graph, but not on the set of arcs of the graph), semisymmetry (a graph is semisymmetric if it is regular, its automorphism group acts transitively on the set of edges and intransitively on the set of vertices of the graph), as well as other algebraic and metric aspects of symmetry in combinatorial objects.