Positivity of Schubert coefficients

Schubert coefficients <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>c</mml:mi> <mml:mrow> <mml:mi>u</mml:mi> <mml:mo>,</mml:mo> <mml:mi>v</mml:mi> </mml:mrow> <mml:mi>w</mml:mi> </mml:msubsup> </mml:math> are structure constants describing multiplication of Schubert polynomials. Deciding positivity of Schubert coefficients is a major open problem in Algebraic Combinatorics. We prove a positive rule for this problem based on two well known assumptions: the Generalized Riemann Hypothesis and the strong derandomization assumption by Miltersen–Vinodchandran.