40 citations · 460 across the 64 of their papers we have counts for
5 papers · 1 filter
Phylogenetic invariants for group-based models
Maria Donten-Bury, Mateusz Michalek
In this paper we investigate properties of algebraic varieties representing group-based phylogenetic models. We propose a method of generating many phylogenetic invariants. We prov…
Family of counterexamples to King's conjecture
Mateusz Michalek
In this short note we present a family of counterexamples to the King's conjecture.
Algebraic varieties representing group-based Markov processes on trees
Mateusz Michalek
In this paper we complete the results of Sullivant and Sturmfels proving that many of the algebraic group-based models for Markov processes on trees are pseudo-toric. We also show…
On the full, strongly exceptional collections on toric varieties with Picard number three
Michal Lason, Mateusz Michalek
We investigate full strongly exceptional collections on smooth, com- plete toric varieties. We obtain explicit results for a large family of varieties with Picard number three, con…
Derived category of toric varieties with Picard number three
Arijit Dey, Michal Lason, Mateusz Michalek
We construct a full, strongly exceptional collection of line bundles on the variety X that is the blow up of the projectivization of the vector bundle O_{P^{n-1}}\oplus O_{P^{n-1}}…