40 citations · 460 across the 64 of their papers we have counts for
8 papers · 1 filter
Complete intersection for equivariant models
M. Casanellas, J. Fernández-Sánchez, M. Michałek
Phylogenetic varieties related to equivariant substitution models have been studied largely in the last years. One of the main objectives has been finding a set of generators of th…
Examples of -regular maps and interpolation spaces
Mateusz Michałek, Christopher Miller
A continous map is -regular if the image of any points spans a -dimensional subspace. It is an important problem in topology an…
Constructions of k-regular maps using finite local schemes
Jarosław Buczyński, Tadeusz Januszkiewicz, Joachim Jelisiejew +1
A continuous map from R^m to R^N or from C^m to C^N is called k-regular if the images of any points are linearly independent. Given integers m and k a problem going back to Che…
Finite phylogenetic complexity of and invariants for
Mateusz Michałek
We study phylogenetic complexity of finite abelian groups - an invariant introduced by Sturmfels and Sullivant. The invariant is hard to compute - so far it was only known for $Z_2…
Obstructions to combinatorial formulas for plethysm
Thomas Kahle, Mateusz Michalek
Motivated by questions of Mulmuley and Stanley we investigate quasi-polynomials arising in formulas for plethysm. We demonstrate, on the examples of and , that…
Abelian Tensors
J. M. Landsberg, Mateusz Michałek
We analyze tensors in the tensor product of three m-dimensional vector spaces satisfying Strassen's equations for border rank m. Results include: two purely geometric characterizat…
Quantum jumps of normal polytopes
Winfried Bruns, Joseph Gubeladze, Mateusz Michałek
We introduce a partial order on the set of all normal polytopes in R^d. This poset NPol(d) is a natural discrete counterpart of the continuum of convex compact sets in R^d, ordered…
Hackbusch Conjecture on tensor formats
Weronika Buczyńska, Jarosław Buczyński, Mateusz Michałek
We prove a conjecture of W. Hackbusch about tensor network states related to a perfect binary tree and train track tree. Tensor network states are used to present seemingly complic…