摘要: We discuss the so-called secant conjecture in real algebraic geometry, and show that it follows from another interesting conjecture, about disconjugacy of vector spaces polynomials one variable.
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A. Eremenko, A. Gabrielov, Elementary proof of the B. and M. Shapiro conjecture for rational functions arXiv: Algebraic Geometry. ,(2005)
A. Eremenko, A. Gabrielov, M. Shapiro, A. Vainshtein, Rational functions and real Schubert calculus Proceedings of the American Mathematical Society. ,vol. 134, pp. 949- 957 ,(2005) , 10.1090/S0002-9939-05-08048-2
Evgeny Mukhin, Vitaly Tarasov, Alexander Varchenko, The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz Annals of Mathematics. ,vol. 170, pp. 863- 881 ,(2009) , 10.4007/ANNALS.2009.170.863
A. Eremenko, A. Gabrielov, Rational functions with real critical points and the B. and M. Shapiro conjecture in real enumerative geometry Annals of Mathematics. ,vol. 155, pp. 105- 129 ,(2002) , 10.2307/3062151
Zach Teitler, Frank Sottile, Luis García-Puente, Abraham M. del Campo, James Ruffo, Stephen L. Johnson, Chris Hillar, Experimentation at the Frontiers of Reality in Schubert Calculus arXiv: Algebraic Geometry. ,vol. 517, ,(2009)
Luis D. García-Puente, Nickolas Hein, Christopher Hillar, Abraham Martín del Campo, James Ruffo, Frank Sottile, Zach Teitler, The Secant Conjecture in the Real Schubert Calculus Experimental Mathematics. ,vol. 21, pp. 252- 265 ,(2012) , 10.1080/10586458.2012.661323
Alexandre Eremenko, Andrei Gabrielov, An Elementary Proof of the B. and M. Shapiro Conjecture for Rational Functions Springer, Basel. pp. 167- 178 ,(2011) , 10.1007/978-3-0348-0142-3_10
E. MUKHIN, V. TARASOV, A. VARCHENKO, ON REALITY PROPERTY OF WRONSKI MAPS Confluentes Mathematici. ,vol. 01, pp. 225- 247 ,(2009) , 10.1142/S1793744209000092