40 citations · 460 across the 64 of their papers we have counts for
7 papers · 1 filter
A tensor version of the quantum Wielandt theorem
Mateusz Michałek, Tim Seynnaeve, Frank Verstraete
We prove boundedness results for the injectivity regions for PEPS. Our result is a higher-dimensional generalization of the quantum Wielandt inequality.
Flag matroids: algebra and geometry
Amanda Cameron, Rodica Dinu, Mateusz Michałek +1
Matroids are ubiquitous in modern combinatorics. As discovered by Gelfand, Goresky, MacPherson and Serganova there is a beautiful connection between matroid theory and the geometry…
Quantum version of Wielandt's Inequality revisited
Mateusz Michałek, Yaroslav Shitov
Consider a linear space L of complex D-dimensional linear operators, and assume that some power L^k of L is the whole space of DxD matrices. Perez-Garcia, Verstraete, Wolf and Cira…
Circulant matrices and Galois-Togliatti systems
Pietro De Poi, Emilia Mezzetti, Mateusz Michałek +2
The goal of this article is to compare the coefficients in the expansion of the permanent with those in the expansion of the determinant of a three-lines circulant matrix. As an ap…
Arithmetic aspects of symmetric edge polytopes
Akihiro Higashitani, Katharina Jochemko, Mateusz Michałek
We investigate arithmetic, geometric and combinatorial properties of symmetric edge polytopes. We give a complete combinatorial description of their facets. By combining Gröbner ba…
Smooth centrally symmetric polytopes in dimension 3 are IDP
Matthias Beck, Christian Haase, Akihiro Higashitani +4
In 1997 Oda conjectured that every smooth lattice polytope has the integer decomposition property. We prove Oda's conjecture for centrally symmetric -dimensional polytopes, by s…
Computing images of polynomial maps
Corey Harris, Mateusz Michałek, Emre Can Sertöz
The image of a polynomial map is a constructible set. While computing its closure is standard in computer algebra systems, a procedure for computing the constructible set itself is…