Name
Title | ||
|---|---|---|
Log-Concave Polynomials III: Mason's Ultra-Log-Concavity Conjecture for Independent Sets of Matroids. |
Abstract | ||
|---|---|---|
We give a self-contained proof of the strongest version of Masonu0027s 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. |
Year | Venue | DocType |
|---|---|---|
2018 | arXiv: Combinatorics | Journal |
Volume | Citations | PageRank |
abs/1811.01600 | 0 | 0.34 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Nima Anari | 1 | 79 | 14.83 |
| Kuikui Liu | 2 | 2 | 2.07 |
| Shayan Oveis Gharan | 3 | 323 | 26.63 |
| Cynthia Vinzant | 4 | 79 | 11.85 |