Lower bounds for real solutions to sparse polynomial systems
By Evgenia Soprunova, Frank Sottile. 2004
50 citations recorded by the source corpus.
We show how to construct sparse polynomial systems that have non-trivial lower bounds on their numbers of real solutions. These are unmixed systems associated to certain polytopes. For the order polytope of a poset P this lower bound is the sign-imbalance of P and it holds if all maximal chains of P have length of the same parity. This theory also gives lower bounds in the real Schubert calculus through the sagbi degeneration of the Grassmannian to a toric variety, and thus recovers a result of Eremenko and Gabrielov.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/f45afb5c335eb1925629420ffad8de34324a1efe
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Discrete Mathematics and Combinatorics
Citations in the corpus
- Intrinsic signs and lower bounds in real algebraic geometry (2011, methodology): “Both the degrees of the Wronski maps in [6] as well as the characteristic of a map in [19] can be understood as the absolute degrees of a relatively orientable map, the obvious analogue of a section in a relatively orientable vector bundle.”