2010/10/04 by Nickolas Hein, Garcia-Puente, Luis, Christopher J. Hillar +10 · 1 citation
Computer Science · Biochemistry, Genetics and Molecular Biology · Medicine · #Polynomial and algebraic computation #Biological Activity of Diterpenoids and Biflavonoids #Cancer Treatment and Pharmacology
paper · pdf · doi:10.48550/arxiv.1010.0665
We formulate the Secant Conjecture, which is a generalization of the Shapiro Conjecture for Grassmannians. It asserts that an intersection of Schubert varieties in a Grassmannian is transverse with all points real, if the flags defining the Schubert varieties are secant along disjoint intervals of a rational normal curve. We present theoretical evidence for it as well as computational evidence obtained in over one terahertz-year of computing, and we discuss some phenomena we observed in our data.