6 papers
On chain polynomials of geometric lattices
Petter Brändén, Leonardo Saud Maia Leite
Athanasiadis and Kalampogia-Evangelinou recently conjectured that the chain polynomial of any geometric lattice has only real zeros. We verify this conjecture for families of geome…
Totally nonnegative matrices, chain enumeration and zeros of polynomials
Petter Brändén, Leonardo Saud Maia Leite
We prove that any lower unitriangular and totally nonnegative matrix gives rise to a family of polynomials with only real zeros. This has consequences for problems in several areas…
Preservation of inequalities under Hadamard products
Petter Brändén, Luis Ferroni, Katharina Jochemko
Wagner (1992) proved that the Hadamard product of two Pólya frequency sequences that are interpolated by polynomials is again a Pólya frequency sequence. We study whether related…
Chow polynomials of totally nonnegative matrices and posets
Petter Brändén, Lorenzo Vecchi
Huh-Stevens and Ferroni-Schröter independently conjectured that Hilbert-Poincaré series of Chow rings of geometric lattices have only real zeros. Ferroni, Matherne and the second…
Chow polynomials of uniform matroids are real-rooted
Petter Brändén, Lorenzo Vecchi
June Huh and Matthew Stevens conjectured that the Hilbert-Poincaré series of the Chow ring of any matroid is a polynomial with only real zeros. We prove this conjecture for the cl…
Lorentzian polynomials
Petter Brändén, June Huh
We study the class of Lorentzian polynomials. The class contains homogeneous stable polynomials as well as volume polynomials of convex bodies and projective varieties. We prove th…