Add to ORKGMonomial ideals are widely studied in commutative algebra. In this thesis, we study a special class of monomial ideals called polymatroidal ideals which admit many nice algebraic and homological properties. They are distinguished by the fact that they satisfy "exchange property" and their powers have linear resolutions. Another important property of polymatroidal ideals is that their monomial localization at any monomial prime ideal is again a polymatroidal ideal. In [1], Bandari and Herzog gave a conjecture that if all monomial localizations of a monomial ideal I have linear resolution then I is polymatroidal. In chapter 4, we discuss persistence and stability properties of polymatroidal ideals and we see that their index of depth stabilit...
soumisInternational audienceWe prove that, for any monoid M, the homology defined by the second auth...
AbstractWhite has conjectured that the toric ideal of a matroid is generated by quadric binomials co...
AbstractLet a={a1⩽a2⩽⋯⩽an} be a sequence of integers or ∞. We introduce a-stable ideals in a polynom...
AbstractAll Cohen–Macaulay polymatroidal ideals are classified. The Cohen–Macaulay polymatroidal ide...
In this dissertation, we study numerical invariants of minimal graded free resolutions of homogeneou...
Let $I$ be a matroidal ideal of degrre $d$ of a polynomial ring $R=K[x_1,...,x_n]$, where $K$ is a f...
AbstractUsing linear algebra methods we study certain algebraic properties of monomial rings and mat...
Let $I$ be a square-free monomial ideal in a polynomial ring $R=K[x_1,\ldots, x_n]$ over a field $K$...
Monomials are the link between Commutative Algebra and Combinatorics. In this thesis we concentrate ...
This work covers three important aspects of monomials ideals in the three chapters "Stanley decompos...
The purpose of this thesis is the study of the symmetric algebra 〖Sym〗_S (L) of an interesting clas...
AbstractWe prove that for any monoid M, the homology defined by the second author by means of polygr...
Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $J$ be a mat...
In this paper we present two different combinatorial approaches to finding resolutions of polynomial...
In this thesis we classify all unmixed monomial ideals I of codimension 2 which are generically a co...
soumisInternational audienceWe prove that, for any monoid M, the homology defined by the second auth...
AbstractWhite has conjectured that the toric ideal of a matroid is generated by quadric binomials co...
AbstractLet a={a1⩽a2⩽⋯⩽an} be a sequence of integers or ∞. We introduce a-stable ideals in a polynom...
AbstractAll Cohen–Macaulay polymatroidal ideals are classified. The Cohen–Macaulay polymatroidal ide...
In this dissertation, we study numerical invariants of minimal graded free resolutions of homogeneou...
Let $I$ be a matroidal ideal of degrre $d$ of a polynomial ring $R=K[x_1,...,x_n]$, where $K$ is a f...
AbstractUsing linear algebra methods we study certain algebraic properties of monomial rings and mat...
Let $I$ be a square-free monomial ideal in a polynomial ring $R=K[x_1,\ldots, x_n]$ over a field $K$...
Monomials are the link between Commutative Algebra and Combinatorics. In this thesis we concentrate ...
This work covers three important aspects of monomials ideals in the three chapters "Stanley decompos...
The purpose of this thesis is the study of the symmetric algebra 〖Sym〗_S (L) of an interesting clas...
AbstractWe prove that for any monoid M, the homology defined by the second author by means of polygr...
Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $J$ be a mat...
In this paper we present two different combinatorial approaches to finding resolutions of polynomial...
In this thesis we classify all unmixed monomial ideals I of codimension 2 which are generically a co...
soumisInternational audienceWe prove that, for any monoid M, the homology defined by the second auth...
AbstractWhite has conjectured that the toric ideal of a matroid is generated by quadric binomials co...
AbstractLet a={a1⩽a2⩽⋯⩽an} be a sequence of integers or ∞. We introduce a-stable ideals in a polynom...