arXiv subjects

Magdaléna Mišinová

Publications and source records attributed to Magdaléna Mišinová.

4 recordsLinked to original sources

arXiv2026

Computing the continuous symmetries of a parametrized variety

We prove that the symmetry Lie algebra of a parametrized variety can be determined directly from the parametrization, without computing the vanishing ideal of the variety. We derive a practical polynomial-time Monte Carlo algorithm for computing the symmetry Lie algebra of a parametrized variety. We discuss applications to testing the binomiality of the ideal of a parametrized variety after changing coordinates, and test this property on varieties arising from staged tree models and colored Gaussian graphical models. Finally, we discuss symmetries and binomiality after changing coordinates for rational curves and give a characterization of the symmetries of many secant varieties.

math.AG↗

arXiv2026

On gamma-vectors and Chow polynomials of restrictions of reflection arrangements

Simplicial arrangements are a special class of hyperplane arrangements, having the property that every chamber is a simplicial cone. It is known that the simpliciality property is preserved under taking restrictions. In this article we focus on the class of reflection arrangements and investigate two different polynomial invariants associated to them and their restrictions, the $h$-polynomial with its $γ$-vector and the Chow polynomial. We prove that all restrictions of reflection arrangements are $γ$-positive and give an explicit combinatorial formula of the Chow polynomial in type $B$. Furthermore we prove that for a special class of restrictions of arrangements of type $D$, called intermediate arrangements, both the $h$-polynomial as well as the Chow polynomial behave arithmetically, that is they interpolate linearly between the respective invariants for type $B$ and $D$.

math.CO↗

arXiv2025

Equivariant Tutte Polynomial

We use the equivariant cohomology ring of the permutohedral variety to study matroids and their invariants. Investigating the pushforward of matroid Chern classes defined by A. Berget, C. Eur, H. Spink and D. Tseng to the product space $\mathbb{P}^n \times \mathbb{P}^n$, we establish an equivariant generalization of the Tutte polynomial of a matroid. This was suggested in a survey paper by M.Michałek. We discuss how this polynomial encodes properties of the matroid by looking at special evaluations. We further introduce an equivariant generalization of the reduced characteristic polynomial of a matroid.

math.AG↗

arXiv2025

Binomiality of colored Gaussian models

Following earlier work by Coons-Maraj-Misra-Sorea and Misra-Sullivant, we study colored, undirected Gaussian graphical models, and present a necessary and sufficient condition for such a model to have binomial vanishing ideal. These conditions involve Jordan schemes, a variant of association schemes, well-known structures in algebraic combinatorics. Using association schemes without transitive group action, we refute the conjecture by Coons-Maraj-Misra-Sorea that binomiality implies that the color classes must be orbits under the automorphism group of the colored graph.

math.CO↗