4 citations · 9 across the 8 of their papers we have counts for
14 papers
A Murnaghan--Nakayama rule for dual stable Grothendieck functions
Dang Tuan Hiep, Do Le Hai Thuy
We give a closed boundary formula for multiplication by power sums in the dual stable Grothendieck basis. The off-diagonal coefficients are signed binomial coefficients supported o…
Enumerative geometry of conics and double covers on projective complete intersections
Dang Tuan Hiep, Ha Thi Thao Tram
We compare genus zero degree two Gromov--Witten invariants with the number of embedded conics on general projective complete intersections whose conic space has expected dimension…
Supersymmetric Schur polynomials have saturated Newton polytopes
Dang Tuan Hiep, Khai-Hoan Nguyen-Dang
We prove that every supersymmetric Schur polynomial has a saturated Newton polytope (SNP). Our approach begins with a tableau-theoretic description of the support, which we encode…
Newton polytope of good symmetric polynomials
Khanh Nguyen Duc, Nguyen Thi Ngoc Giao, Dang Tuan Hiep +1
We introduce a general class of symmetric polynomials that have saturated Newton polytope and their Newton polytope has integer decomposition property. The class covers numerous pr…
A characterization of the algebraic degree in semidefinite programming
Dang Tuan Hiep, Nguyen Thi Ngoc Giao, Nguyen Thi Mai Van
In this article, we show that the algebraic degree in semidefinite programming can be expressed in terms of the coefficient of a certain monomial in a doubly symmetric polynomial.…
A Murnaghan-Nakayama rule for Grothendieck polynomials of Grassmannian type
Khanh Nguyen Duc, Dang Tuan Hiep, Tran Ha Son +1
We consider the Grothendieck polynomials appearing in the K-theory of Grassmannians, which are analogs of Schur polynomials. This paper aims to establish a version of the Murnaghan…
An identity involving symmetric polynomials and the geometry of Lagrangian Grassmannians
Dang Tuan Hiep
We first prove an identity involving symmetric polynomials. This identity leads us into exploring the geometry of Lagrangian Grassmannians. As an insight applications, we obtain a…
Identities involving (doubly) symmetric polynomials and integrals over Grassmannians
Dang Tuan Hiep
We obtain identities involving symmetric and doubly symmetric polynomials. These identities provide a way of handling expressions appearing in the Atiyah-Bott-Berline-Vergne formul…
Numerical invariants of Fano schemes of linear subspaces on complete intersections
Dang Tuan Hiep
The goal of this paper is to explore the genus and degree of the Fano scheme of linear subspaces on a complete intersection in a complex projective space. Firstly, suppose that the…
A formula for the algebraic degree in semidefinite programming
Dang Tuan Hiep
In this paper we use the Bott residue formula in equivariant cohomology to show a formula for the algebraic degree in semidefinite programming.
On the degree of Fano schemes of linear subspaces on hypersurfaces
Dang Tuan Hiep
In this paper we propose and prove an explicit formula for computing the degree of Fano schemes of linear subspaces on general hypersurfaces. The method used here is based on the l…
Rational Curves on Calabi-Yau Threefolds: Verifying Mirror Symmetry Predictions
Dang Tuan Hiep
In this paper, the numbers of rational curves on general complete intersection Calabi-Yau threefolds in complex projective spaces are computed up to degree six. The results are all…
Computing Serre's intersection multiplicities
Dang Tuan Hiep
The aim of this note is to describe how to compute the intersection multiplicity defined by Jean Pierre Serre.
Representations of non-negative polynomials via critical ideals
Dang Tuan Hiep
This paper studies the representations of a non-negative polynomial on a non-compact semi-algebraic set modulo its critical ideal. Under the assumptions that the semi-algeb…