8 papers
Multivalued Groups and Schur Rings
A. V. Vasil'ev, I. N. Ponomarenko
We study finite involutive multivalued groups associated with Schur rings. Their reduced valency is shown to equal the least common multiple of the sizes of the basic sets of the c…
Notes on -groups
Ilia Ponomarenko, Grigory Ryabov
Following Wielandt, a finite group is called a -group (Burnside group) if every primitive group containing a regular subgroup isomorphic to is doubly transitive. Using a…
Cartesian products of graphs and their coherent configurations
Jinzhuan Cai, Jin Guo, Alexander L. Gavrilyuk +1
The coherent configuration of a graph is the smallest coherent configuration on the vertices of that contains the edge set of as a relation. The aim of…
On multivalued groups of order 3
Jin Guo, Ilia Ponomarenko, Andrey V. Vasil'ev
A complete classification of the multivalued coset groups of order is given. The proof is based on the classification of rank groups having regular normal subgroups.
A linear programming bound for sum-rank metric codes
Aida Abiad, Alexander L. Gavrilyuk, Antonina P. Khramova +1
We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances,…
Closures of permutation groups with restricted nonabelian composition factors
Ilia Ponomarenko, Saveliy V. Skresanov, Andrey V. Vasil'ev
Given a permutation group on a finite set , let denote the -closure of , that is, the largest permutation group on having the same orbits in the induced…
On the Weisfeiler-Leman dimension of circulant graphs
Yulai Wu, Ilia Ponomarenko
A circulant graph is a Cayley graph of a finite cyclic group. The Weisfeiler-Leman-dimension of a circulant graph with respect to the class of all circulant graphs is the small…
A large family of strongly regular graphs with small Weisfeiler-Leman dimension
Jinzhuan Cai, Jin Guo, Alexander L. Gavrilyuk +1
In 2002, D. Fon-Der-Flaass constructed a prolific family of strongly regular graphs. In this paper, we prove that for infinitely many natural numbers , this family contains $n^{…