The monotone secant conjecture in the real Schubert calculus
Hein N, Hillar C, Martin del Campo Sanchez A, Sottile F, Teitler Z. 2015. The monotone secant conjecture in the real Schubert calculus. Experimental Mathematics. 24(3), 261–269.
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Author
Hein, Nicolas;
Hillar, Christopher;
Martin del Campo Sanchez, AbrahamISTA;
Sottile, Frank;
Teitler, Zach
Department
Abstract
The monotone secant conjecture posits a rich class of polynomial systems, all of whose solutions are real. These systems come from the Schubert calculus on flag manifolds, and the monotone secant conjecture is a compelling generalization of the Shapiro conjecture for Grassmannians (Theorem of Mukhin, Tarasov, and Varchenko). We present some theoretical evidence for this conjecture, as well as computational evidence obtained by 1.9 teraHertz-years of computing, and we discuss some of the phenomena we observed in our data.
Publishing Year
Date Published
2015-06-23
Journal Title
Experimental Mathematics
Volume
24
Issue
3
Page
261 - 269
IST-REx-ID
Cite this
Hein N, Hillar C, Martin del Campo Sanchez A, Sottile F, Teitler Z. The monotone secant conjecture in the real Schubert calculus. Experimental Mathematics. 2015;24(3):261-269. doi:10.1080/10586458.2014.980044
Hein, N., Hillar, C., Martin del Campo Sanchez, A., Sottile, F., & Teitler, Z. (2015). The monotone secant conjecture in the real Schubert calculus. Experimental Mathematics. Taylor & Francis. https://doi.org/10.1080/10586458.2014.980044
Hein, Nicolas, Christopher Hillar, Abraham Martin del Campo Sanchez, Frank Sottile, and Zach Teitler. “The Monotone Secant Conjecture in the Real Schubert Calculus.” Experimental Mathematics. Taylor & Francis, 2015. https://doi.org/10.1080/10586458.2014.980044.
N. Hein, C. Hillar, A. Martin del Campo Sanchez, F. Sottile, and Z. Teitler, “The monotone secant conjecture in the real Schubert calculus,” Experimental Mathematics, vol. 24, no. 3. Taylor & Francis, pp. 261–269, 2015.
Hein N, Hillar C, Martin del Campo Sanchez A, Sottile F, Teitler Z. 2015. The monotone secant conjecture in the real Schubert calculus. Experimental Mathematics. 24(3), 261–269.
Hein, Nicolas, et al. “The Monotone Secant Conjecture in the Real Schubert Calculus.” Experimental Mathematics, vol. 24, no. 3, Taylor & Francis, 2015, pp. 261–69, doi:10.1080/10586458.2014.980044.
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