27 citations · 68 across the 17 of their papers we have counts for
14 papers · 1 filter
Polytope volume by descent in the face lattice and applications in social choice
Winfried Bruns, Bogdan Ichim
We describe the computation of polytope volumes by descent in the face lattice, its implementation in Normaliz, and the connection to reverse-lexicographic triangulations. The effi…
On the behavior of the size of a monomial ideal
Bogdan Ichim, Andrei Zarojanu
In this paper we study the behavior of the size of a monomial ideal under polarization and under generic deformations. As an application, we extend a result relating the size and t…
How to compute the Stanley depth of a module
Bogdan Ichim, Lukas Katthän, Julio José Moyano-Fernández
In this paper we introduce an algorithm for computing the Stanley depth of a finitely generated multigraded module over the polynomial ring . As a…
Lcm-lattices and Stanley depth: a first computational approach
Bogdan Ichim, Lukas Katthän, Julio José Moyano-Fernández
Let be a field, and let be the polynomial ring. Let be a monomial ideal of with up to 5 generators. In this paper, we present a c…
Stanley depth and the lcm-lattice
Bogdan Ichim, Lukas Katthän, Julio José Moyano-Fernández
In this paper we show that the Stanley depth, as well as the usual depth, are essentially determined by the lcm-lattice. More precisely, we show that for quotients of monomia…
The behavior of Stanley depth under polarization
Bogdan Ichim, Lukas Katthän, Julio José Moyano-Fernández
Let be a field, be the polynomial ring and two monomial ideals in . In this paper we show that $\mathrm{sdepth}\ {I/J} - \mathrm{depth}…
An algorithm for computing the multigraded Hilbert depth of a module
Bogdan Ichim, Andrei Zarojanu
A method for computing the multigraded Hilbert depth of a module was presented in [16]. In this paper we improve the method and we introduce an effective algorithm for performing t…
How to compute the multigraded Hilbert depth of a module
Bogdan Ichim, Julio José Moyano-Fernández
The aim of this paper is to introduce a method for computing Hilbert decompositions (and consequently the Hilbert depth) of a finitely generated multigraded module over the pol…
Normaliz: Algorithms for Affine Monoids and Rational Cones
Winfried Bruns, Bogdan Ichim
Normaliz is a program for solving linear systems of inequalities. In this paper we present the algorithms implemented in the program, starting with version 2.0.
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,…
On toric face rings
Bogdan Ichim, Tim Roemer
Following a construction of Stanley we consider toric face rings associated to rational pointed fans. This class of rings is a common generalization of the concepts of Stanley--Rei…
On the Coefficients of Hilbert Quasipolynomials
Winfried Bruns, Bogdan Ichim
The Hilbert function of a module over a positively graded algebra is of quasi-polynomial type (Hilbert--Serre). We derive an upper bound for its grade, i.e. the index from which on…
Length Formulas for the Homology of Generalized Koszul Complexes
Bogdan Ichim, Udo Vetter
Let be a finite module over a noetherian ring with a free resolution of length 1. We consider the generalized Koszul complexes associated with a ma…
Koszul Bicomplexes and Generalized Koszul Complexes in Projective Dimension One
Bogdan Ichim, Udo Vetter
We describe Koszul type complexes associated with a linear map from any module to a free module, and vice versa with a linear map from a free module to an arbitrary module, general…