Kuikui Liu
Massachusetts Institute of Technology · Electrical Engineering & Computer Science
Active 2006–2024
Research topics
- Mathematics
- Combinatorics
Selected publications
Log-concave polynomials III: Mason’s ultra-log-concavity conjecture for independent sets of matroids
Proceedings of the American Mathematical Society · 2024 · 23 citations
- Combinatorics
- Mathematics
We give a self-contained proof of the strongest version of Mason’s conjecture, namely that for any matroid the sequence of the number of independent sets of given sizes is ultra log-concave. To do this, we introduce a class of polynomials, called completely log-concave polynomials, whose bivariate restrictions have ultra log-concave coefficients. At the heart of our proof we show that for any matroid, the homogenization of the generating polynomial of its independent sets is completely log-concave.
Frequent coauthors
- 16 shared
Shayan Oveis Gharan
- 14 shared
Nima Anari
- 10 shared
Cynthia Vinzant
- 9 shared
Eric Vigoda
University of California, Santa Barbara
- 9 shared
Zongchen Chen
University at Buffalo, State University of New York
- 6 shared
David X. Wu
- 5 shared
Xueyan Zhang
Hubei University of Arts and Science
- 4 shared
Amit Rajaraman
IIT@MIT
- Resume-aware match score
- Save to shortlist
- AI-drafted outreach
See your match with Kuikui Liu
PhdFit ranks faculty by your research interests, methods, and publications — grounded in their actual work, not templates.
- Free to start
- No credit card
- 30-second signup