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

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

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10.1016/j.jcta.2017.06.003

Cite this

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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.",

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AU - Payne, Sam

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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

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JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

ER -

Combinatorial and inductive methods for the tropical maximal rank conjecture

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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