40 citations · 460 across the 64 of their papers we have counts for
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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…
Many faces of symmetric edge polytopes
Alessio D'Alì, Emanuele Delucchi, Mateusz Michałek
Symmetric edge polytopes are a class of lattice polytopes constructed from finite simple graphs. In the present paper we highlight their connections to the Kuramoto synchronization…
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…
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…
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…
Phylogenetic complexity of the Kimura 3-parameter model
Mateusz Michałek, Emanuele Ventura
In algebraic statistics, the Kimura 3-parameter model is one of the most interesting and classical phylogenetic models. We prove that the ideals associated to this model are genera…
Interlacing Ehrhart Polynomials of Reflexive Polytopes
Akihiro Higashitani, Mario Kummer, Mateusz Michałek
It was observed by Bump et al. that Ehrhart polynomials in a special family exhibit properties similar to the Riemann ζ function. The construction was generalized by Matsui et al.…
Finite phylogenetic complexity and combinatorics of tables
Mateusz Michałek, Emanuele Ventura
We prove that the phylogenetic complexity -- an invariant introduced by Sturmfels and Sullivant -- of any finite abelian group is finite.
The poset of rational cones
Joseph Gubeladze, Mateusz Michałek
We introduce a natural partial order on the set Cones(d) of rational cones in R^d. The poset NPol(d-1) of normal polytopes in R^{d-1} embeds into Cones(d) via the homogenization ma…
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…
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…
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…
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…
Very ample and Koszul segmental fibrations
Matthias Beck, Jessica Delgado, Joseph Gubeladze +1
In the hierarchy of structural sophistication for lattice polytopes, normal polytopes mark a point of origin; very ample and Koszul polytopes occupy bottom and top spots in this hi…
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…
On the graph labellings arising from phylogenetics
Weronika Buczyńska, Jarosław Buczyński, Kaie Kubjas +1
We study semigroups of labellings associated to a graph. These generalize the Jukes-Cantor model and phylogenetic toric varieties defined by Buczyńska. Our main theorem bounds the…
A short proof of Combinatorial Nullstellensatz
Mateusz Michalek
In this note we give a short, direct proof of the well known Combinatorial Nullstellensatz.