Matyas Domokos
Research Subjects
Matyas Domokos has a total of 40 co-authors. Here are the top co-authors by number of shared publications:
- Vesselin Drensky
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
9 shared publications - Kálmán Cziszter
Alfréd Rényi Institute of Mathematics Hungarian Academy of Sciences Reáltanoda utca 13-15 1053 Budapest Hungary
6 shared publications - T. H. Lenagan
University of Edinburgh
6 shared publications - Alexander N. Zubkov
Omsk State Pedagogical University
3 shared publications - Dániel Joó
Rényi Institute of Mathematics Hungarian Academy of Sciences Budapest Hungary
3 shared publications - István Szöllősi
Faculty of Mathematics and Computer Science Babeş-Bolyai University M. Kogălniceanu 1 400084 Cluj-Napoca, Romania and Faculty of Informatics Eötvös Loránd University Pázmány P. 1/C H-1117 Budapest, Hungary
3 shared publications
Latest Publications
- 12 October 2026
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 753, 546-568
Degeneration order of 3 × 3 nilpotent matrix tuples
- 12 October 2026
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 753, 546-568
Degeneration order of 3 × 3 nilpotent matrix tuples
- Open Access
- 25 March 2026
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- p. 1-20
Exponential valuations on lattice polygons
We classify translatively exponential and $\mathrm {GL}(2,\mathbb Z)$ covariant valuations on lattice polygons with values in the space of real (complex) measurable functions. A typical example of such valuations is induced by the Laplace transform, but as it turns out there are many more. The argument uses the ergodicity of the linear action of $\mathrm {SL}(2,\mathbb Z)$ on $\mathbb R^2$ , and some elementary properties of the Fibonacci numbers.- 25 March 2026
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- p. 1-20
Open AccessExponential valuations on lattice polygons
We classify translatively exponential and $\mathrm {GL}(2,\mathbb Z)$ covariant valuations on lattice polygons with values in the space of real (complex) measurable functions. A typical example of such valuations is induced by the Laplace transform, but as it turns out there are many more. The argument uses the ergodicity of the linear action of $\mathrm {SL}(2,\mathbb Z)$ on $\mathbb R^2$ , and some elementary properties of the Fibonacci numbers. - Open Access
- 11 March 2026
- Published by Elsevier in Applied and Computational Harmonic Analysis
- Vol. 84
Separating polynomial invariants over non-closed fields of finite abelian groups
- 11 March 2026
- Published by Elsevier in Applied and Computational Harmonic Analysis
- Vol. 84
Open AccessSeparating polynomial invariants over non-closed fields of finite abelian groups
- 23 December 2025
- Published by Institute of Mathematics and Informatics Bulgarian Academy of Sciences in Serdica Mathematical Journal
- Vol. 51 (3–4)
On the cones of classical groups
The cone of a classical group \(G\) is an affine \(G\times G\)-variety. The aim of this note is to initiate its combinatorial study in the cases when \(G\) is the complex orthogonal or symplectic group (the case of the general linear group being well documented in the literature). The coordinate ring of the cone of G is a finitely generated commutative graded algebra. First the \(G\times G\)-module structure of its homogeneous components is determined. This is used to compute the Hilbert series of this coordinate ring in the cases when G is the orthogonal group \(\mathrm{O}(3)\), \(\mathrm{O}(4)\), the special orthogonal group \(\mathrm{SO}(4)\), and when \(G\) is the symplectic group \(\mathrm{Sp}(4)\). It is concluded that the coordinate ring of the cone of \(\mathrm{O}(3)\) is not Koszul, hence the vanishing ideal of this cone has no quadratic Gr¨obner basis (although it is minimally generated by quadratic elements).- 23 December 2025
- Published by Institute of Mathematics and Informatics Bulgarian Academy of Sciences in Serdica Mathematical Journal
- Vol. 51 (3–4)
On the cones of classical groups
The cone of a classical group \(G\) is an affine \(G\times G\)-variety. The aim of this note is to initiate its combinatorial study in the cases when \(G\) is the complex orthogonal or symplectic group (the case of the general linear group being well documented in the literature). The coordinate ring of the cone of G is a finitely generated commutative graded algebra. First the \(G\times G\)-module structure of its homogeneous components is determined. This is used to compute the Hilbert series of this coordinate ring in the cases when G is the orthogonal group \(\mathrm{O}(3)\), \(\mathrm{O}(4)\), the special orthogonal group \(\mathrm{SO}(4)\), and when \(G\) is the symplectic group \(\mathrm{Sp}(4)\). It is concluded that the coordinate ring of the cone of \(\mathrm{O}(3)\) is not Koszul, hence the vanishing ideal of this cone has no quadratic Gr¨obner basis (although it is minimally generated by quadratic elements).- Open Access
Separating versus ordinary Noether numbers
Let $G$ be a finite group and $K$ a field containing an element of multiplicative order $|G|$. It is shown that if $G$ has a cyclic subgroup of index at most $2$, then the separating Noether number over $K$ of $G$ coincides with the Noether number over $K$ of $G$. The same conclusion holds when $G$ is the direct product of a dihedral group and the $2$-element group. On the other hand, the smallest non-abelian groups $G$ are found for which the separating Noether number over $K$ is strictly less than the Noether number over $K$. Along the way the exact value of the separating Noether number is determined for all groups of order at most $16$. The results show in particular that unlike the ordinary Noether number, the separating Noether number of a non-abelian finite group may well be equal to the separating Noether number of a proper direct factor of the group.Open AccessSeparating versus ordinary Noether numbers
Let $G$ be a finite group and $K$ a field containing an element of multiplicative order $|G|$. It is shown that if $G$ has a cyclic subgroup of index at most $2$, then the separating Noether number over $K$ of $G$ coincides with the Noether number over $K$ of $G$. The same conclusion holds when $G$ is the direct product of a dihedral group and the $2$-element group. On the other hand, the smallest non-abelian groups $G$ are found for which the separating Noether number over $K$ is strictly less than the Noether number over $K$. Along the way the exact value of the separating Noether number is determined for all groups of order at most $16$. The results show in particular that unlike the ordinary Noether number, the separating Noether number of a non-abelian finite group may well be equal to the separating Noether number of a proper direct factor of the group. - Open Access
Exponential valuations on lattice polygons valued at formal power series
We classify valuations on lattice polygons with values in the ring of formal power series that commute with the action of the affine unimodular group. A typical example of such valuations is induced by the Laplace transform, but as it turns out there are many more. The classification is done in terms of formal power series that satisfy certain functional equations. We align our classification with the decomposition into so-called dilative components.
Open AccessExponential valuations on lattice polygons valued at formal power series
We classify valuations on lattice polygons with values in the ring of formal power series that commute with the action of the affine unimodular group. A typical example of such valuations is induced by the Laplace transform, but as it turns out there are many more. The classification is done in terms of formal power series that satisfy certain functional equations. We align our classification with the decomposition into so-called dilative components.
- Open Access
On the cones of classical groups
The cone of a classical group $G$ is an affine $G\times G$-variety. The aim of this note is to initiate its combinatorial study in the cases when $G$ is the complex orthogonal or symplectic group. The coordinate ring of the cone of $G$ is a finitely generated commutative graded algebra. First the $G\times G$-module structure of its homogeneous components is determined. This is used to compute the Hilbert series of this coordinate ring in the cases when $G$ is the orthogonal group $\mathrm{O}(3)$, $\mathrm{O}(4)$, the special orthogonal group $\mathrm{SO}(4)$, and when $G$ is the symplectic group $\mathrm{Sp}(4)$. It is concluded that the coordinate ring of the cone of $\mathrm{O}(3)$ is not Koszul, hence the vanishing ideal of this cone has no quadratic Gröbner basis (although it is minimally generated by quadratic elements).Open AccessOn the cones of classical groups
The cone of a classical group $G$ is an affine $G\times G$-variety. The aim of this note is to initiate its combinatorial study in the cases when $G$ is the complex orthogonal or symplectic group. The coordinate ring of the cone of $G$ is a finitely generated commutative graded algebra. First the $G\times G$-module structure of its homogeneous components is determined. This is used to compute the Hilbert series of this coordinate ring in the cases when $G$ is the orthogonal group $\mathrm{O}(3)$, $\mathrm{O}(4)$, the special orthogonal group $\mathrm{SO}(4)$, and when $G$ is the symplectic group $\mathrm{Sp}(4)$. It is concluded that the coordinate ring of the cone of $\mathrm{O}(3)$ is not Koszul, hence the vanishing ideal of this cone has no quadratic Gröbner basis (although it is minimally generated by quadratic elements). - Open Access
Separating polynomial invariants over non-closed fields of finite abelian groups
It is proved that for any finite dimensional representation of a prime order group over the field of rational numbers, polynomial invariants of degree at most $3$ separate the orbits. A result providing an upper degree bound for separating invariants for representations of finite abelian groups over algebraically closed base fields of non-modular characteristic is generalized for the case of base fields that are not algebraically closed (like the fields of real or rational numbers).Open AccessSeparating polynomial invariants over non-closed fields of finite abelian groups
It is proved that for any finite dimensional representation of a prime order group over the field of rational numbers, polynomial invariants of degree at most $3$ separate the orbits. A result providing an upper degree bound for separating invariants for representations of finite abelian groups over algebraically closed base fields of non-modular characteristic is generalized for the case of base fields that are not algebraically closed (like the fields of real or rational numbers). - 11 May 2025
- Published by Springer Nature
- p. 1-17
The Directed Cayley Diameter and the Davenport Constant
- 11 May 2025
- Published by Springer Nature
- p. 1-17
The Directed Cayley Diameter and the Davenport Constant
- 12 August 2024
- Published by European Mathematical Society - EMS - Publishing House GmbH in Journal of Combinatorial Algebra
Quiver moduli spaces of a given dimension
It is shown that certain transformations on quiver-dimension vector pairs induce isomorphisms on the corresponding moduli spaces of quiver representations and map a stable dimension vector to a stable dimension vector. This result combined with a combinatorial analysis of dimension vectors in the fundamental set of a wild quiver is applied to prove that in each dimension there are only finitely many projective algebraic varieties occurring as a moduli space of representations of a quiver with a dimension vector that satisfies some simple constraints.
- 12 August 2024
- Published by European Mathematical Society - EMS - Publishing House GmbH in Journal of Combinatorial Algebra
Quiver moduli spaces of a given dimension
It is shown that certain transformations on quiver-dimension vector pairs induce isomorphisms on the corresponding moduli spaces of quiver representations and map a stable dimension vector to a stable dimension vector. This result combined with a combinatorial analysis of dimension vectors in the fundamental set of a wild quiver is applied to prove that in each dimension there are only finitely many projective algebraic varieties occurring as a moduli space of representations of a quiver with a dimension vector that satisfies some simple constraints.