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math.CO2025
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…
math.CO2025
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…
math.CO2025
Order polytopes of crown posets
Teemu Lundström, Leonardo Saud Maia Leite
In the last decade, the order polytope of the zigzag poset has been thoroughly studied. A related poset, called \emph{crown poset}, obtained by adding an extra relation between the…