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arXiv · 1308.4381

Lower Bounds in Real Schubert Calculus

Nickolas Hein·Christopher J. Hillar·Frank Sottile
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Abstract

We describe a large-scale computational experiment to study structure in the numbers of real solutions to osculating instances of Schubert problems. This investigation uncovered Schubert problems whose computed numbers of real solutions variously exhibit nontrivial upper bounds, lower bounds, gaps, and a congruence modulo four. We present a family of Schubert problems, one in each Grassmannian, and prove their osculating instances have the observed lower bounds and gaps.

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Nickolas Hein, Christopher J. Hillar, Frank Sottile. 2013-08-20. Lower Bounds in Real Schubert Calculus. https://arxiv.org/abs/1308.4381

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