34 citations · 97 across the 11 of their papers we have counts for
11 papers
Empty simplices of large width
Joseph Doolittle, Lukas Katthän, Benjamin Nill +1
An empty simplex is a lattice simplex in which vertices are the only lattice points. We show two constructions leading to the first known empty simplices of width larger than their…
Spanning Lattice Polytopes and the Uniform Position Principle
Johannes Hofscheier, Lukas Katthän, Benjamin Nill
A lattice polytope is called IDP if any lattice point in its th dilate is a sum of lattice points in . In 1991 Stanley proved a strong inequality in Ehrhart theory fo…
The Koszul homology algebra of the second Veronese is generated by the lowest strand
Aldo Conca, Lukas Katthän, Victor Reiner
We show that the Koszul homology algebra of the second Veronese subalgebra of a polynomial ring over a field of characteristic zero is generated, as an algebra, by the homology cla…
The structure of DGA resolutions of monomial ideals
Lukas Katthän
Let be a squarefree monomial ideal a polynomial ring. In this paper we study multiplications on the minimal free resolution of $k[x_1,…
Ehrhart Theory of Spanning Lattice Polytopes
Johannes Hofscheier, Lukas Katthän, Benjamin Nill
A lattice polytope is called spanning if its lattice points affinely span the ambient lattice. We show as a corollary to a general result in the Ehrhart theory of lattice polytopes…
Which series are Hilbert series of graded modules over polynomial rings?
Lukas Katthän, Julio José Moyano-Fernández, Jan Uliczka
Let be a multigraded polynomial ring such that the degree of each variable is a unit vector; so is the homogeneous coordinate ring of a product of projective spaces. In thi…