arXiv subjects

Samuel Lundqvist

Publications and source records attributed to Samuel Lundqvist.

25 records · Page 2Linked to original sources

arXiv2016

On the structure of monomial complete intersections in positive characteristic

In this paper we study the Lefschetz properties of monomial complete intersections in positive characteristic. We give a complete classification of the strong Lefschetz property when the number of variables is at least three, which proves a conjecture by Cook II. We also extend earlier results on the weak Lefschetz property by dropping the assumption on the residue field being infinite, and by giving new sufficient criteria.

math.AC↗

arXiv2015

Non-vanishing forms in projective space over finite fields

We consider a subset of projective space over a finite field and give bounds on the minimal degree of a non-vanishing form with respect to this subset.

math.AG↗

arXiv2015

Boolean ideals and their varieties

We consider ideals in the ring $\mathbb{Z}_2[x_1,\ldots, x_n]$ that contain the polynomials $x_i^2 - x_i$ for $i = 1, \ldots, n$ and give various results related to the one-to-one correspondence between these ideals and the subsets of $\mathbb{Z}_2^n$. We also study the standard monomials with respect to the lexicographical ordering for these ideals and derive a distribution result.

math.AC↗

arXiv2013

A Gorenstein numerical semi-group ring having a transcendental series of Betti numbers

We prove in particular that the Gorenstein numerical semigroup ring generated by (36,48,50,52,56,60,66,67,107,121,129,135) has a transcendental series of Betti numbers. The methods of proofs are the theory of Golod homomorphism and the theory of infinite positively graded Lie algebras. This paper is more than twice as long as earlier 1212.0720, has two extra authors and has new general results about decomposition of graded Lie algebras (theorems 2,3 and 4) in the new section 4.

math.AC↗

arXiv2009

Vector space bases associated to vanishing ideals of points

We discuss four different constructions of vector space bases associated to vanishing ideals of points. We show how to compute normal forms with respect to these bases and give new complexity bounds. As an application, we improve the computational algebra approach to the reverse engineering of gene regulatory networks.

math.AC↗

arXiv2009

Multiplication matrices and ideals of projective dimension zero

We introduce the concept of multiplication matrices for ideals of projective dimension zero. We discuss various applications and in particular, we give a new algorithm to compute the variety of an ideal of projective dimension zero.

math.AG↗

arXiv2008

Complexity of comparing monomials and two improvements of the BM-algorithm

We give a new algorithm for merging sorted lists of monomials. Together with a projection technique we obtain a new complexity bound for the BM-algorithm.

math.AC↗