32 citations · 116 across the 16 of their papers we have counts for
20 papers
Lefschetz properties of balanced 3-polytopes
David Cook, Martina Juhnke-Kubitzke, Satoshi Murai +1
In this paper, we study Lefschetz properties of Artinian reductions of Stanley-Reisner rings of balanced simplicial -polytopes. A -dimensional simplicial complex is said…
Some algebras with the weak Lefschetz property
David Cook, Uwe Nagel
Using a connection to lozenge tilings of triangular regions, we establish an easily checkable criterion that guarantees the weak Lefschetz property of a quotient by a monomial idea…
Syzygy bundles and the weak Lefschetz property of almost complete intersections
David Cook, Uwe Nagel
Deciding the presence of the weak Lefschetz property often is a challenging problem. In this work an in-depth study is carried out in the case of Artinian monomial ideals with four…
The weak Lefschetz property for monomial ideals of small type
David Cook, Uwe Nagel
In this work a combinatorial approach towards the weak Lefschetz property is developed that relates this property to enumerations of signed perfect matchings as well as to enumerat…
Signed lozenge tilings
David Cook, Uwe Nagel
It is well-known that plane partitions, lozenge tilings of a hexagon, perfect matchings on a honeycomb graph, and families of non-intersecting lattice paths in a hexagon are all in…
An algebraic approach to finite projective planes
David Cook, Juan Migliore, Uwe Nagel +1
A finite projective plane, or more generally a finite linear space, has an associated incidence complex that gives rise to two natural algebras: the Stanley-Reisner ring an…