67 citations · 256 across the 18 of their papers we have counts for
18 papers
The Gröbner Version of White's Conjecture is False
Spencer Backman, Nathan Cheung, Michał Lasoń +2
We show that the toric ideal of the Fano matroid polytope does not have a quadratic Gröbner basis. This resolves in the negative a strong version of White's conjecture from matroid…
Quantitative properties of the non-properness set of a polynomial map, a positive characteristic case
Zbigniew Jelonek, Michał Lasoń
Let be a generically finite polynomial map of degree between affine spaces. In arXiv:1411.5011 we proved that if is the fie…
Stillman's conjecture via generic initial ideals
Jan Draisma, Michal Lason, Anton Leykin
Using recent work by Erman-Sam-Snowden, we show that finitely generated ideals in the ring of bounded-degree formal power series in infinitely many variables have finitely generate…
List coloring of matroids and base exchange properties
Michał Lasoń
A coloring of a matroid is an assignment of colors to the elements of its ground set. We restrict to proper colorings - those for which elements of the same color form an independe…
Quantitative properties of the non-properness set of a polynomial map
Zbigniew Jelonek, Michał Lasoń
Let be a generically finite polynomial map of algebraic degree . Motivated by the study of the Jacobian Conjecture, we prove that the set $…
Non-normal very ample polytopes - constructions and examples
Michał Lasoń, Mateusz Michałek
We present a method of constructing non-normal very ample polytopes as a segmental fibration of unimodular graph polytopes. In many cases we explicitly compute their invariants - H…
Coloring intersection graphs of arc-connected sets in the plane
Michał Lasoń, Piotr Micek, Arkadiusz Pawlik +1
A family of sets in the plane is simple if the intersection of its any subfamily is arc-connected, and it is pierced by a line if the intersection of its any member with is…
A generalization of Combinatorial Nullstellensatz
Michał Lasoń
In this note we give an extended version of Combinatorial Nullstellensatz, with weaker assumption on nonvanishing monomial. We also present an application of our result in a situat…
f-vectors implying vertex decomposability
Michał Lasoń
We prove that if a pure simplicial complex of dimension d with n facets has the least possible number of (d-1)-dimensional faces among all complexes with n faces of dimension d, th…
Indicated coloring of matroids
Michał Lasoń
A coloring of a matroid is proper if elements of the same color form an independent set. For a loopless matroid M, its chromatic number χ(M) is the minimum number of colors that su…
Coloring Hypergraphs Induced by Dynamic Point Sets and Bottomless Rectangles
Andrei Asinowski, Jean Cardinal, Nathann Cohen +9
We consider a coloring problem on dynamic, one-dimensional point sets: points appearing and disappearing on a line at given times. We wish to color them with k colors so that at an…
On-line list coloring of matroids
Michał Lasoń, Wojciech Lubawski
A coloring of a matroid is proper if elements of the same color form an independent set. A theorem of Seymour asserts that a k-colorable matroid is also colorable from any lists of…
Triangle-free geometric intersection graphs with large chromatic number
Arkadiusz Pawlik, Jakub Kozik, Tomasz Krawczyk +4
Several classical constructions illustrate the fact that the chromatic number of a graph can be arbitrarily large compared to its clique number. However, until very recently, no su…
The coloring game on matroids
Michał Lasoń
A coloring of the ground set of a matroid is proper if elements of the same color form an independent set. For a loopless matroid , its chromatic number is the minimum nu…
Triangle-free intersection graphs of line segments with large chromatic number
Arkadiusz Pawlik, Jakub Kozik, Tomasz Krawczyk +4
In the 1970s, Erdos asked whether the chromatic number of intersection graphs of line segments in the plane is bounded by a function of their clique number. We show the answer is n…
An extremal problem on crossing vectors
Michał Lasoń, Piotr Micek, Noah Streib +2
For positive integers and , two vectors and from are called -crossing if there are two coordinates and such that and $B[j…
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}}…