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Real Stability and Log Concavity are coNP-Complete
- Publication Year :
- 2024
-
Abstract
- Real-stable, Lorentzian, and log-concave polynomials are well-studied classes of polynomials, and have been powerful tools in resolving several conjectures. We show that the problems of deciding whether a polynomial of fixed degree is real stable or log concave are coNP-complete. On the other hand, while all homogeneous real-stable polynomials are Lorentzian and all Lorentzian polynomials are log concave on the positive orthant, the problem of deciding whether a polynomial of fixed degree is Lorentzian can be solved in polynomial time.<br />Comment: 21 pages, 1 figure
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2405.00162
- Document Type :
- Working Paper