100 citations · 291 across the 51 of their papers we have counts for
37 papers · 1 filter
-graded rings and their canonical modules
Margherita Barile, Winfried Bruns
In ``Cohen--Macaulay rings'' Bruns and Herzog define the graded canonical module for -graded rings. We generalize the definition to multigradings and prove that the c…
Sagbi bases, defining ideals and algebra of minors
Winfried Bruns, Aldo Conca, Francesca Lembo
This paper extends the article of the Bruns and Conca on SAGBI bases and their computation (J. Symb. Comput. 120 (2024)) in two directions. (i) We describe the extension of the Sin…
A New Invariant of Lattice polytopes
Winfried Bruns, Takayuki Hibi
The maximal degree of monomials belonging to the unique minimal system of monomial generators of the canonical module of the toric ring defin…
Sagbi combinatorics of maximal minors and a Sagbi algorithm
Winfried Bruns, Aldo Conca
The maximal minors of a matrix of indeterminates are a universal Gröbner basis by a theorem of Bernstein, Sturmfels and Zelevinsky. On the other hand it is known that they are not…
Castelnuovo-Mumford regularity and powers
Winfried Bruns, Aldo Conca, Matteo Varbaro
This note has two goals. The first is to give a short and self contained introduction to the Castelnuovo-Mumford regularity for standard graded ring over a general base ring. T…
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…
A remark on regularity of powers and products of ideals
Winfried Bruns, Aldo Conca
New title and minor adjustments. To appear in the Journal of Pure and Applied Algebra
Linear resolutions of powers and products
Winfried Bruns, Aldo Conca
The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of…
Hilbert Regularity of Stanley-Reisner Rings
Winfried Bruns, Hero Saremi
In this note, we characterize the Hilbert regularity of the Stanley-Reisner ring in terms of the -vector and the -vector of a simplicial complex $\bigtria…
Products of Borel fixed ideals of maximal minors
Winfried Bruns, Aldo Conca
We study a large family of products of Borel fixed ideals of maximal minors. We compute their initial ideals and primary decompositions, and show that they have linear free resolut…
Hilbert regularity of ZZ-graded modules over polynomial rings
Winfried Bruns, Julio José Moyano-Fernández, Jan Uliczka
Let M be a finitely generated ZZ-graded module over the standard graded polynomial ring R=K[X_1, ..., X_n] with K a field, and let H_M(t)=Q_M(t)/(1-t)^d be the Hilbert series of M.…
Ideals generated by superstandard tableaux
Andrew Berget, Winfried Bruns, Aldo Conca
We investigate products J of ideals of "row initial" minors in the polynomial ring K[X] defined by a generic m-by-n matrix. Such ideals are shown to be generated by a certain set o…
Maximal minors and linear powers
Winfried Bruns, Aldo Conca, Matteo Varbaro
An ideal I in a polynomial ring S has linear powers if all the powers I^k of I have a linear free resolution. We show that the ideal of maximal minors of a sufficiently general mat…
Relations between the minors of a generic matrix
Winfried Bruns, Aldo Conca, Matteo Varbaro
It is well-known that the Plücker relations generate the ideal of relations of the maximal minors of a generic matrix. In this paper we discuss the relations between minors of a (n…
Hilbert depth of powers of the maximal ideal
Winfried Bruns, Christian Krattenthaler, Jan Uliczka
The Hilbert depth of a module M is the maximum depth that occurs among all modules with the same Hilbert function as M. In this note we compute the Hilbert depths of the powers of…
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.
Stanley decompositions and Hilbert depth in the Koszul complex
Winfried Bruns, Christian Krattenthaler, Jan Uliczka
Stanley decompositions of multigraded modules over polynomials rings have been discussed intensively in recent years. There is a natural notion of depth that goes with a Stanle…
A Macaulay 2 interface for Normaliz
Winfried Bruns, Gesa Kaempf
Normaliz is a tool for the computation of Hilbert bases of normal affine monoids and related tasks. We describe the Macaulay 2 interface to Normaliz. It makes Normaliz accessible f…
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-…
Gröbner bases and Betti numbers of monoidal complexes
Winfried Bruns, Robert Koch, Tim Roemer
In this note we consider monoidal complexes and their associated algebras, called toric face rings. These rings generalize Stanley-Reisner rings and affine monoid algebras. We comp…
The variety of exterior powers of linear maps
Winfried Bruns, Aldo Conca
Let be a field and and be -vector spaces of dimension and . Let be the canonical map from to . We investigate the Z…
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…
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…
On seminormal monoid rings
Winfried Bruns, Ping Li, Tim Roemer
Given a seminormal affine monoid M we consider several monoid properties of M and their connections to ring properties of the associated affine monoid ring K[M] over a field K. We…