40 citations · 66 across the 13 of their papers we have counts for
16 papers
Modularity of minor-free graphs
Michał Lasoń, Małgorzata Sulkowska
We prove that a class of graphs with an excluded minor and with the maximum degree sublinear in the number of edges is maximally modular, that is, modularity tends to 1 as the numb…
A note on seminormality of cut polytopes
Michał Lasoń, Mateusz Michałek
We prove that seminormality of cut polytopes is equivalent to normality. This settles two conjectures regarding seminormality of cut polytopes.
Gorenstein matroids
Michał Lasoń, Mateusz Michałek
Matroid base polytope and independence polytope are Cohen-Macaulay. There are plenty of examples when they are also Gorenstein. We provide a full classification of matroids whose i…
Optimal stopping for many connected components in a graph
Michał Lasoń
We study a new optimal stopping problem: Let be a fixed graph with vertices which become active on-line in time, one by another, in a random order. The active part of i…
Gorenstein graphic matroids
Takayuki Hibi, Michał Lasoń, Kazunori Matsuda +2
The toric variety of a matroid is projectively normal, and therefore it is Cohen-Macaulay. We provide a complete graph-theoretic classification when the toric variety of a graphic…
Matroid multiple cyclic exchange property
Michał Lasoń
We prove a new exchange property for bases of a matroid that generalizes the multiple symmetric exchange property. For every bases of a matroid and a subset $A_1\su…
On the toric ideals of matroids of a fixed rank
Michał Lasoń
In White conjectured that every element of the toric ideal of a matroid is generated by quadratic binomials corresponding to symmetric exchanges. We prove White's conjecture…
Cox rings of du Val singularities
Laura Facchini, Víctor González-Alonso, Michał Lasoń
In this note we introduce Cox rings of singularities and explicitly compute them in the case of du Val singularities and .
Coloring games and algebraic problems on matroids
Michał Lasoń
This thesis is basically devoted to matroids -- fundamental structure of combinatorial optimization -- though some of our results concern simplicial complexes, or Euclidean spaces.…
-uniruled sets in affine geometry
Michał Lasoń
The main goal of this thesis is to study -uniruled sets that appear in affine geometry. At the beginning we discuss the property of -uniruledness and its eq…
Splitting necklaces and measurable colorings of the real line
Noga Alon, Jarosław Grytczuk, Michał Lasoń +1
A (continuous) necklace is simply an interval of the real line colored measurably with some number of colors. A well-known application of the Borsuk-Ulam theorem asserts that every…
On the relation between Betti numbers of an Arf semigroup and its blowup
Michał Lasoń
In this note we prove the relation between Betti numbers of an Arf semigroup and its blowup in the case when they have the same multiplicity . The relation is then $β_{…
Equivalent condition for approximately Cohen-Macaulay complexes
Michał Lasoń
We give a necessary and sufficient condition for a simplicial complex to be approximately Cohen-Macaulay. Namely it is approximately Cohen-Macaulay if and only if the ideal associa…
The set of fixed points of a unipotent group
Zbigniew Jelonek, Michał Lasoń
Let be an algebraically closed field. Let be a non-trivial connected unipotent group, which acts effectively on an affine variety Then every non-empty component of…
Obstacles for splitting multidimensional necklaces
Michał Lasoń
The well-known "necklace splitting theorem" of Alon asserts that every -colored necklace can be fairly split into parts using at most cuts, provided . In a…
On the toric ideal of a matroid
Michał Lasoń, Mateusz Michałek
Describing minimal generating set of a toric ideal is a well-studied and difficult problem. In 1980 White conjectured that the toric ideal associated to a matroid is equal to the i…