4. Total Positivity
Unfortunately, this conjecture has been found to be false, and so these pages
are nolonger relevant.
The preceding sections have dealt with Schubert conditions given by flags
osculating a real rational normal curve.
Recently, Shapiro and Shapiro have extended their conjecture, generalizing
this choice of flags.
This generalization involves totally positive matrices.
Here, we describe that generalization and present some computational
evidence in support of that extended conjecture.
Unfortunately, this conjecture has been found to be false, and so these pages
are nolonger relevant.
-
Total positivity and the conjecture of Shapiro and Shapiro.
-
Parameterization of totally positive matrices.
-
Computational evidence.
5.
Further remarks.