7 citations · 13 across the 18 of their papers we have counts for
5 papers · 1 filter
Koszul multi-Rees algebras of principal -Borel Ideals
Michael DiPasquale, Babak Jabbar Nezhad
Given a monomial in a polynomial ring and a subset of the variables of the polynomial ring, the principal -Borel ideal generated by is the ideal generated by all mon…
A lower bound for the dimension of tetrahedral splines in large degree
Michael DiPasquale, Nelly Villamizar
We derive a formula which is a lower bound on the dimension of trivariate splines on a tetrahedral partition which are continuously differentiable of order in large enough degr…
A lower bound for splines on tetrahedral vertex stars
Michael DiPasquale, Nelly Villamizar
A tetrahedral complex all of whose tetrahedra meet at a common vertex is called a \textit{vertex star}. Vertex stars are a natural generalization of planar triangulations, and unde…
On resurgence via asymptotic resurgence
Michael DiPasquale, Ben Drabkin
The resurgence and asymptotic resurgence of an ideal in a polynomial ring are two statistics which measure the relationship between its regular and symbolic powers. We address two…
Counting the dimension of splines of mixed smoothness: A general recipe, and its application to meshes of arbitrary topologies
Deepesh Toshniwal, Michael DiPasquale
In this paper we study the dimension of bivariate polynomial splines of mixed smoothness on polygonal meshes. Here, "mixed smoothness" refers to the choice of different orders of s…