6 citations · 21 across the 13 of their papers we have counts for
16 papers
The path-missing and path-free complexes of a directed graph
Darij Grinberg, Lukas Katthän, Joel Brewster Lewis
We study two simplicial complexes arising from a directed graph with two chosen vertices and : the *path-free complex*, consisting of all subsets $F \subseteq E…
The Lecture Hall Cone as a toric deformation
Lukas Katthän
The Lecture Hall cone is a simplicial cone whose lattice points naturally correspond to Lecture Hall partitions. The celebrated Lecture Hall Theorem of Bousquet-Mélou and Eriksson…
On f- and h- vectors of relative simplicial complexes
Giulia Codenotti, Lukas Katthän, Raman Sanyal
A relative simplicial complex is a collection of sets of the form , where are simplicial complexes. Relative complexes played key roles in recent advance…
The Homology of Connective Morava -theory with coefficients in
Lukas Katthän, Sean Tilson
Let be the connective cover of the Morava -theory spectrum of height . In this paper we compute its homology for any prime and $n \leq…
Linear maps in minimal free resolutions of Stanley-Reisner rings
Lukas Katthän
In this short note we give an elementary description of the linear part of the minimal free resolution of a Stanley-Reisner ring of a simplicial complex . Indeed, the differenti…
The Symmetric signature of cyclic quotient singularities
Alessio Caminata, Lukas Katthän
The symmetric signature is an invariant of local domains which was recently introduced by Brenner and the first author in an attempt to find a replacement for the -signature in…
A non-Golod ring with a trivial product on its Koszul homology
Lukas Katthän
We present a monomial ideal such that is not Golod, even though the product on its Koszul homology is trivial. This constitutes a countere…
Betti posets and the Stanley depth
Lukas Katthän
Let be a polynomial ring and let be a monomial ideal. In this short note, we propose the conjecture that the Betti poset of determines the Stanley projectiv…
A Canonical module characterization of Serre's
Lukas Katthän, Kohji Yanagawa
In this short note, we give a characterization of domains satisfying Serre's condition in terms of their canonical modules. In the special case of toric rings, thi…
The Golod property for Stanley-Reisner rings in varying characteristic
Lukas Katthän
We show that the Golod property of a Stanley-Reisner ring can depend on the characteristic of the base field. More precisely, for every finite set of prime numbers we construct…
Stanley depth and simplicial spanning trees
Lukas Katthän
We show that for proving the Stanley conjecture, it is sufficient to consider a very special class of monomial ideals. These ideals (or rather their lcm lattices) are in bijection…
Two lower bounds for the Stanley depth of monomial ideals
Lukas Katthän, Seyed Amin Seyed Fakhari
Let be two monomial ideals of the polynomial ring . In this paper, we provide two lower bounds for the Stanley depth of . On t…
Non-normal affine monoids
Lukas Katthän
We give a geometric description of the set of holes in a non-normal affine monoid . The set of holes turns out to be related to the non-trivial graded components of the local co…
Decomposing Sets of Inversions
Lukas Katthän
In this note we consider the question how the set of inversions of a permutation can be partitioned into two subset, such that those are itself inversion sets of permuta…
The Linear Ordering Polytope via Representations
Lukas Katthän
Let denote the -th linear ordering polytope. We define projections from to the -th permutahedron and to the -st linear ordering polytope. Both projections…
On homology spheres with few minimal non faces
Lukas Katthän
Let Δbe a (d-1)-dimensional homology sphere on n vertices with m minimal non-faces. We consider the invariant α:= m - (n-d) and prove that for a given value of α, there are only fi…