Combinatorial and inductive methods for the tropical maximal rank conjecture

David Jensen; Sam Payne

doi:10.1016/j.jcta.2017.06.003

Combinatorial and inductive methods for the tropical maximal rank conjecture

David Jensen, Sam Payne

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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	https://doi.org/10.1016/j.jcta.2017.06.003
State	Published - Nov 2017

Bibliographical note

Funding Information:
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 .

Publisher Copyright:
© 2017 Elsevier Inc.

Keywords

Maximal rank conjecture
Tropical geometry
Tropical independence

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Access to Document

10.1016/j.jcta.2017.06.003

Cite this

@article{9b2a63e0a38741df826752ac5ea7c3bd,

title = "Combinatorial and inductive methods for the tropical maximal rank conjecture",

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.",

keywords = "Maximal rank conjecture, Tropical geometry, Tropical independence",

author = "David Jensen and Sam Payne",

note = "Funding Information: 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 . Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

month = nov,

doi = "10.1016/j.jcta.2017.06.003",

language = "English",

volume = "152",

pages = "138--158",

}

TY - JOUR

T1 - Combinatorial and inductive methods for the tropical maximal rank conjecture

AU - Jensen, David

AU - Payne, Sam

N1 - Funding Information: 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 . Publisher Copyright: © 2017 Elsevier Inc.

PY - 2017/11

Y1 - 2017/11

N2 - 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.

AB - 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.

KW - Maximal rank conjecture

KW - Tropical geometry

KW - Tropical independence

UR - http://www.scopus.com/inward/record.url?scp=85033395310&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85033395310&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2017.06.003

DO - 10.1016/j.jcta.2017.06.003

M3 - Article

AN - SCOPUS:85033395310

VL - 152

SP - 138

EP - 158

ER -

Combinatorial and inductive methods for the tropical maximal rank conjecture

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this