100 citations · 333 across the 26 of their papers we have counts for
18 papers · 1 filter
Simplicial complexes in network intrusion profiling
Mandala von Westenholz, Martin Atzmueller, Tim Römer
For studying intrusion detection data we consider data points referring to individual IP addresses and their connections: We build networks associated with those data points, such…
Algebraic properties of Levi graphs associated with curve arrangements
Piotr Pokora, Tim Römer
In the present paper we study algebraic properties of edge ideals associated with plane curve arrangements via their Levi graphs. Using combinatorial properties of such Levi graphs…
Classes of cut ideals and their Betti numbers
Jürgen Herzog, Masoomeh Rahimbeigi, Tim Römer
We study monomial cut ideals associated to a graph , which are a monomial analogue of toric cut ideals as introduced by Sturmfels and Sullivant. Primary decompositions, projecti…
Asymptotic behavior of symmetric ideals: A brief survey
Martina Juhnke-Kubitzke, Dinh Van Le, Tim Römer
Recently, chains of increasing symmetric ideals have attracted considerable attention. In this note, we summarize some results and open problems concerning the asymptotic behavior…
Learning algebraic decompositions using Prony structures
Stefan Kunis, Tim Römer, Ulrich von der Ohe
We propose an algebraic framework generalizing several variants of Prony's method and explaining their relations. This includes Hankel and Toeplitz variants of Prony's method for t…
FI- and OI-modules with varying coefficients
Uwe Nagel, Tim Römer
We introduce FI-algebras over a commutative ring and the category of FI-modules over an FI-algebra. Such a module may be considered as a family of invariant modules over compat…
Retracts and algebraic properties of cut algebras
Tim Roemer, Sara Saeedi Madani
We study cut algebras which are toric rings associated to graphs. The key idea is to consider suitable retracts to understand algebraic properties and invariants of such algebras l…
Equivariant Hilbert Series in non-Noetherian Polynomial Rings
Uwe Nagel, Tim Roemer
We introduce and study equivariant Hilbert series of ideals in polynomial rings in countably many variables that are invariant under a suitable action of a symmetric group or the m…
Absolutely Koszul algebras and the Backelin-Roos property
Aldo Conca, Srikanth B. Iyengar, Hop D. Nguyen +1
We study absolutely Koszul algebras, Koszul algebras with the Backelin-Roos property and their behavior under standard algebraic operations. In particular, we identify some Verones…
Criteria for componentwise linearity
Uwe Nagel, Tim Roemer
We establish characteristic-free criteria for the componentwise linearity of graded ideals. As applications, we classify the componentwise linear ideals among the Gorenstein ideals…
Koszul cycles
Winfreid Bruns, Aldo Conca, Tim Römer
We prove regularity bounds for Koszul cycles holding for every ideal of dimension at most 1 in a polynomial ring. We generalize the lower bound for the Green-Lazarsfeld index of Ve…
Algebraic Properties of Generic Tropical Varieties
Tim Roemer, Kirsten Schmitz
We show that the algebraic invariants multiplicity and depth of a graded ideal in the polynomial ring are closely connected to the fan structure of its generic tropical variety in…
Generic Tropical Varieties
Tim Roemer, Kirsten Schmitz
We show that in the constant coefficient case the generic tropical variety of a graded ideal exists. This can be seen as the analogon to the existence of the generic initial ideal…
Koszul homology and syzygies of Veronese subalgebras
Winfried Bruns, Aldo Conca, Tim Roemer
A graded K-algebra R has property N_p if it is generated in degree 1, has relations in degree 2 and the syzygies of order less or equal to p on the relations are linear. The Green-…
Linearity defects of modules over commutative rings
Srikanth B. Iyengar, Tim Roemer
This article concerns linear parts of minimal resolutions of finitely generated modules over commutative local, or graded rings. The focus is on the linearity defect of a module, w…
On canonical modules of toric face rings
Bogdan Ichim, Tim Roemer
Generalizing the concepts of Stanley-Reisner and affine monoid algebras, one can associate to a rational pointed fan the toric face ring. Assuming that this ring is Cohen-Macaulay,…
h-vectors of Gorenstein polytopes
Winfried Bruns, Tim Roemer
We show that the Ehrhart h-vector of an integer Gorenstein polytope with a regular unimodular triangulation satisfies McMullen's g-theorem; in particular, it is unimodal. This resu…
The Multiplicity Conjecture in low codimensions
Juan C. Migliore, Uwe Nagel, Tim Römer
We establish the multiplicity conjecture of Herzog, Huneke, and Srinivasan about the multiplicity of graded Cohen-Macaulay algebras over a field, for codimension two algebras and f…