Abstract
We produce new combinatorial methods for approaching the tropical maximal rank conjecture, including inductive procedures for deducing new cases of the conjecture on graphs of increasing genus from any given case. Using explicit calculations in a range of base cases, we prove this conjecture for the canonical divisor, and in a wide range of cases for m=3, extending previous results for m=2.
| Original language | English |
|---|---|
| Pages (from-to) | 138-158 |
| Number of pages | 21 |
| Journal | Journal of Combinatorial Theory. Series A |
| Volume | 152 |
| DOIs | |
| State | Published - Nov 2017 |
Bibliographical note
Publisher Copyright:© 2017 Elsevier Inc.
Funding
We have benefited from a number of helpful conversations with colleagues during the preparation of this work, and wish to thank, in particular, T. Feng, C. Fontanari, E. Larson, and L. Sauermann. The work of DJ is partially supported by National Science Foundation DMS-1601896 and that of SP by National Science Foundation CAREER DMS-1149054 .
| Funders | Funder number |
|---|---|
| U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China | DMS-1601896, 1149054 |
Keywords
- Maximal rank conjecture
- Tropical geometry
- Tropical independence
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics