9 citations · 38 across the 13 of their papers we have counts for
8 papers · 1 filter
Noetherian Operators in Macaulay2
Justin Chen, Yairon Cid-Ruiz, Marc Härkönen +2
A primary ideal in a polynomial ring can be described by the variety it defines and a finite set of Noetherian operators, which are differential operators with polynomial coefficie…
Average Behavior of Minimal Free Resolutions of Monomial Ideals
Jesús A. De Loera, Serkan Hoşten, Robert Krone +1
We describe the typical homological properties of monomial ideals defined by random generating sets. We show that, under mild assumptions, random monomial ideals (RMI's) will almos…
Equivariant Gröbner bases
Christopher J. Hillar, Robert Krone, Anton Leykin
Algorithmic computation in polynomial rings is a classical topic in mathematics. However, little attention has been given to the case of rings with an infinite number of variables…
Hilbert series of symmetric ideals in infinite polynomial rings via formal languages
Robert Krone, Anton Leykin, Andrew Snowden
Let be the polynomial ring where and , and let be an ideal of stable under the natural action of the infinite symmetric g…
Equivariant Gröbner bases of symmetric toric ideals
Robert Krone
It has been shown previously that a large class of monomial maps equivariant under the action of an infinite symmetric group have finitely generated kernels up to the symmetric act…
Numerical Hilbert functions for Macaulay2
Robert Krone
The NumericalHilbert package for Macaulay2 includes algorithms for computing local dual spaces of polynomial ideals, and related local combinatorial data about its scheme structure…