Zobrazeno 1 - 10
of 200
pro vyhledávání: '"Schenck, Hal"'
We investigate algebraic and topological signatures of networks of coupled oscillators. Translating dynamics into a system of algebraic equations enables us to identify classes of network topologies that exhibit unexpected behaviors. Many previous st
Externí odkaz:
http://arxiv.org/abs/2312.16069
We describe the minimal free resolution of the ideal of $2 \times 2$ subpermanents of a $2 \times n$ generic matrix $M$. In contrast to the case of $2 \times 2$ determinants, the $2 \times 2$ permanents define an ideal which is neither prime nor Cohe
Externí odkaz:
http://arxiv.org/abs/2312.12247
This survey gives an overview of three central algebraic themes related to the study of splines: duality, group actions, and homology. Splines are piecewise polynomial functions of a prescribed order of smoothness on some subdivided domain D in R^k,
Externí odkaz:
http://arxiv.org/abs/2312.09829
Autor:
Grate, Sean, Schenck, Hal
We study the Artinian reduction $A$ of a configuration of points $X \subset {\mathbb P}^n $, and the relation of the geometry of $X$ to Lefschetz properties of $A$. Migliore initiated the study of this connection, with a particular focus on the Hilbe
Externí odkaz:
http://arxiv.org/abs/2307.13126
Autor:
Abdallah, Nancy, Schenck, Hal
A net in $\mathbb{P}^2$ is a configuration of lines $\mathcal A$ and points $X$ satisfying certain incidence properties. Nets appear in a variety of settings, ranging from quasigroups to combinatorial design to classification of Kac-Moody algebras to
Externí odkaz:
http://arxiv.org/abs/2208.01557
Autor:
Abdallah, Nancy, Schenck, Hal
In 1978, Stanley constructed an example of an Artinian Gorenstein (AG) ring $A$ with non-unimodal $H$-vector $(1,13,12,13,1)$. Migliore-Zanello later showed that for regularity $r=4$, Stanley's example has the smallest possible codimension $c$ for an
Externí odkaz:
http://arxiv.org/abs/2208.01536
Autor:
Kapustka, Gregorz, Kapustka, Michał, Ranestad, Kristian, Schenck, Hal, Stillman, Mike, Yuan, Beihui
A quaternary quartic form, a quartic form in four variables, is the dual socle generator of an Artinian Gorenstein ring of codimension and regularity 4. We present a classification of quartic forms in terms of rank and powersum decompositions which c
Externí odkaz:
http://arxiv.org/abs/2111.05817
We study real bihomogeneous polynomials $r(z,\bar{z})$ in $n$ complex variables for which $r(z,\bar{z}) \|z\|^2$ is the squared norm of a holomorphic polynomial mapping. Such polynomials are the focus of the Sum of Squares Conjecture, which describes
Externí odkaz:
http://arxiv.org/abs/2111.03192
Autor:
Abdallah, Nancy, Schenck, Hal
Publikováno v:
In Journal of Symbolic Computation March-April 2024 121