  We consider real
  polynomials in one variable without vanishing coefficients and with
  all roots real and of distinct moduli.
  We show that the signs of the coefficients define the order of
  the moduli of the roots on the real positive half-line exactly when no four
  consecutive signs of coefficients equal $(+,+,-,-)$, $(-,-,+,+)$,
  $(+,-,-,+)$ or $(-,+,+,-)$.
