7 citations · 17 across the 9 of their papers we have counts for
11 papers
Invariant chains of graphs
Do Trong Hoang, Mitra Koley, Dinh Van Le
We initiate a systematic study of Inc-invariant chains of graphs, the combinatorial counterparts of Inc-invariant chains of edge ideals arising in the theory of equivariant Noether…
Duality of monoids up to symmetry
Dinh Van Le, Tim Römer, Nguyen Thi Vien
We study duality for monoids in an infinite-dimensional setting that are invariant under the action of the infinite symmetric group Sym. Our main result is an equivariant Minkowski…
On monoids up to symmetry
Dinh Van Le, Tim Römer, Nguyen Thi Vien
We study monoids in an infinite-dimensional setting that are invariant under the action of the infinite symmetric group Sym. Our main result establishes a local--global principle c…
Asymptotic depth of invariant chains of edge ideals
Tran Quang Hoa, Do Trong Hoang, Dinh Van Le +2
We completely determine the asymptotic depth, equivalently, the asymptotic projective dimension of a chain of edge ideals that is invariant under the action of the monoid Inc of in…
Equivariant lattice bases
Dinh Van Le, Tim Römer
We study lattices in free abelian groups of infinite rank that are invariant under the action of the infinite symmetric group, with emphasis on finiteness of their equivariant base…
On regularity and projective dimension of invariant chains of monomial ideals
Dinh Van Le, Hop D. Nguyen
Ideals in infinite-dimensional polynomial rings that are invariant under the action of the monoid of increasing functions have been extensively studied recently. Of particular inte…
Theorems of Carathéodory, Minkowski-Weyl, and Gordan up to symmetry
Dinh Van Le, Tim Römer
In this paper we extend three classical and fundamental results in polyhedral geometry, namely, Carathéodory's theorem, the Minkowski-Weyl theorem, and Gordan's lemma to infinite d…
Invariant chains in algebra and discrete geometry
Thomas Kahle, Dinh Van Le, Tim Römer
We relate finite generation of cones, monoids, and ideals in increasing chains (the local situation) to equivariant finite generation of the corresponding limit objects (the global…
Flawlessness of -vectors of broken circuit complexes
Martina Juhnke-Kubitzke, Le Van Dinh
One of the major open questions in matroid theory asks whether the -vector of the broken circuit complex of a matroid satisfies the following inequali…
On the Orlik--Terao ideal and the relation space of a hyperplane arrangement
Le Van Dinh, Fatemeh Mohammadi
The relation space of a hyperplane arrangement is the vector space of all linear dependencies among the defining forms of the hyperplanes in the arrangement. In this paper, we stud…
On the Gorensteinness of broken circuit complexes and Orlik--Terao ideals
Le Van Dinh
It is proved that the broken circuit complex of an ordered matroid is Gorenstein if and only if it is a complete intersection. Several characterizations for a matroid that admits s…