40 citations · 99 across the 23 of their papers we have counts for
18 papers · 1 filter
Isomorphism Criterion of Monomial Digraphs over Prime Fields
Alexander M. Kodess, Felix Lazebnik, Mikhail Muzychuk
For any Galois field with elements and any positive integers and , the directed graph has vertex set , and ther…
Fusions of tensor powers of Johnson schemes
Sean Eberhard, Mikhail Muzychuk
This paper is a follow-up to (arXiv:2203.03687), in which the first author studied primitive association schemes lying between a tensor power of the trivial assoc…
CI-property of and for digraphs
István Kovács, Mikhail Muzychuk, Péter P. Pálfy +2
We prove that the direct product of two coprime order elementary abelian groups of rank two, as well as the direct product of a cyclic group of prime order and a cyclic group of sq…
Generalised dihedral CI-groups
Ted Dobson, Mikhail Muzychuk, Pablo Spiga
In this paper, we find a strong new restriction on the structure of CI-groups. We show that, if is a generalised dihedral group and if is a CI-group, then for every odd pri…
A classification of one dimensional affine rank three graphs
M. Muzychuk
The rank three subgroups of a one-dimensional affine group over a finite field were classified in 1978 by Foulser and Kallaher. Although one can use their results for a classificat…
On Jordan schemes
Mikhail Muzychuk, Sven Reichard, Mikhail Klin
In 2003 Peter Cameron introduced the concept of a Jordan scheme and asked whether there exist Jordan schemes which are not symmetrisations of coherent configurations (proper Jordan…
Proper Jordan schemes exist. First examples, computer search, patterns of reasoning. An essay
Mikhail Klin, Mikhail Muzychuk, Sven Reichard
A special class of Jordan algebras over a field of characteristic zero is considered. Such an algebra consists of an -dimensional subspace of the vector space of all square…
Testing isomorphism of circulant objects in polynomial time
Mikhail Muzychuk, Ilia Ponomarenko
Let be a class of combinatorial objects invariant with respect to a given regular cyclic group. It is proved that the isomorphism of any two objects c…
The Cayley isomorphism property for Cayley maps
Mikhail Muzychuk, Gábor Somlai
In this paper we study finite groups which have Cayley isomorphism property with respect to Cayley maps, CIM-groups for a brief. We show that the structure of the CIM-groups is ver…
Cyclic groups are CI-groups for balanced configurations
Hiroki Koike, István Kovács, Dragan Marušič +1
In this paper it is shown that every finite cyclic group satisfies the CI-property for the class of balanced configurations.
On Schur 2-groups
Mikhail Muzychuk, Ilya Ponomarenko
A finite group is called a Schur group, if any Schur ring over is the transitivity module of a point stabilizer in a subgroup of $\sym(G)$ that contains all right translati…
A solution of an equivalence problem for semisimple cyclic codes
M. Muzychuk
In this paper we propose an efficient solution of an equivalence problem for semisimple cyclic codes.
On Skew Hadamard difference sets
Mikhail Muzychuk
In this paper we construct exponentionally many non-isomorphic skew Hadamard difference sets over an elementary abelian group of order .
On quasi-thin association schemes
M. Muzychuk, I. Ponomarenko
An association scheme is called quasi-thin if the valency of each its basic relation is one or two. A quasi-thin scheme is Kleinian if the thin residue of it forms a Klein group wi…
Uniformity in association schemes and coherent configurations: cometric Q-antipodal schemes and linked systems
Edwin R. van Dam, William J. Martin, Mikhail E. Muzychuk
Inspired by some intriguing examples, we study uniform association schemes and uniform coherent configurations, including cometric Q-antipodal association schemes. After a review o…
On Pseudocyclic Association Schemes
M. E. Muzychuk, I. N. Ponomarenko
The notion of pseudocyclic association scheme is generalized to the non-commutative case. It is proved that any pseudocyclic scheme the rank of which is much more than the valency…
Strongly regular Cayley graphs over primary abelian groups of rank 2
Yefim I. Leifman, Mikhail E. Muzychuk
Strongly regular Cayley graphs with Paley parameters over abelian groups of rank 2 were studied in [J.A Davis, Partial difference sets in p-groups, Arch.Math.63 (1994) 103-110; K.H…
Symmetric Bush-type Hadamard matrices of order exist for all odd
Mikhail Muzychuk, Qing Xiang
Using reversible Hadamard difference sets, we construct symmetric Bush-type Hadamard matrices of order for all odd integer .