6 citations · 21 across the 13 of their papers we have counts for
7 papers · 1 filter
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…
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…
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…