Add to ORKGIn this paper we present two different combinatorial approaches to finding resolutions of polynomial ideals. Their goal is to get resolutions that are as small as possible while still preserving the structure of the zeroth syzygy module. Then we present the idea of a differential graded algebra and discuss when the minimal resolutions of a polynomial ideals admits such a structure
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.Cataloged from PD...
Abstract. For a graph G, we construct two algebras whose dimensions are both equal to the number of ...
Free resolutions for an ideal are constructions that tell us useful information about the structure ...
We construct the minimal resolutions of three classes of monomial ideals: dominant, 1-semidominant, ...
In recent years, the combinatorial properties of monomials ideals and binomial ideals have been wide...
AbstractWe provide a new combinatorial approach to study the minimal free resolutions of edge ideals...
Abstract: The relationships between the generators of an ideal encapsulate a great deal of informati...
In this dissertation, we study numerical invariants of minimal graded free resolutions of homogeneou...
AbstractWe study the minimal free resolution of a quadratic monomial ideal in the case where the res...
summary:For each squarefree monomial ideal $I\subset S = k[x_{1},\ldots , x_{n}] $, we associate a s...
This work covers three important aspects of monomials ideals in the three chapters "Stanley decompos...
The question we address in this paper is: which monomial ideals have minimal cellular resolutions, t...
AbstractLet a={a1⩽a2⩽⋯⩽an} be a sequence of integers or ∞. We introduce a-stable ideals in a polynom...
We construct cellular resolutions for monomial ideals via discrete Morse theory. In particular, we d...
We investigate algebra structures on resolutions of a special class of Cohen-Macaulay simplicial com...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.Cataloged from PD...
Abstract. For a graph G, we construct two algebras whose dimensions are both equal to the number of ...
Free resolutions for an ideal are constructions that tell us useful information about the structure ...
We construct the minimal resolutions of three classes of monomial ideals: dominant, 1-semidominant, ...
In recent years, the combinatorial properties of monomials ideals and binomial ideals have been wide...
AbstractWe provide a new combinatorial approach to study the minimal free resolutions of edge ideals...
Abstract: The relationships between the generators of an ideal encapsulate a great deal of informati...
In this dissertation, we study numerical invariants of minimal graded free resolutions of homogeneou...
AbstractWe study the minimal free resolution of a quadratic monomial ideal in the case where the res...
summary:For each squarefree monomial ideal $I\subset S = k[x_{1},\ldots , x_{n}] $, we associate a s...
This work covers three important aspects of monomials ideals in the three chapters "Stanley decompos...
The question we address in this paper is: which monomial ideals have minimal cellular resolutions, t...
AbstractLet a={a1⩽a2⩽⋯⩽an} be a sequence of integers or ∞. We introduce a-stable ideals in a polynom...
We construct cellular resolutions for monomial ideals via discrete Morse theory. In particular, we d...
We investigate algebra structures on resolutions of a special class of Cohen-Macaulay simplicial com...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.Cataloged from PD...
Abstract. For a graph G, we construct two algebras whose dimensions are both equal to the number of ...
Free resolutions for an ideal are constructions that tell us useful information about the structure ...