Totally positive polynomials with small length

In this work we provide a list of irreducible monic, totally positive polynomials with integer coefficients and lengths below 2.3679d for a degree d polynomial. Our approach combines techniques based on auxiliary functions and mixed-integer linear programming algorithms. The list obtained shows that there are polynomials of this type up to degree 16, with the exception of degree 11 where we are very close to the threshold.

---

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).