scholarly journals A positive formula for the Ehrhart-like polynomials from root system chip-firing

2019 ◽  
Vol 2 (6) ◽  
pp. 1159-1196 ◽  
Author(s):  
Sam Hopkins ◽  
Alexander Postnikov
Keyword(s):  
Root System ◽  
Positive Formula ◽  
Chip Firing

scholarly journals Root system chip-firing I: interval-firing

2018 ◽  
Vol 292 (3-4) ◽  
pp. 1337-1385 ◽  
Author(s):  
Pavel Galashin ◽  
Sam Hopkins ◽  
Thomas McConville ◽  
Alexander Postnikov
Keyword(s):  
Root System ◽  
Chip Firing

scholarly journals Root System Chip-Firing II: Central-Firing

2019 ◽  
Author(s):  
Pavel Galashin ◽  
Sam Hopkins ◽  
Thomas McConville ◽  
Alexander Postnikov
Keyword(s):  
Weyl Group ◽  
Root System ◽  
Dynkin Diagram ◽  
Positive Root ◽  
Root Systems ◽  
Initial Weight ◽  
Fundamental Weight ◽  
Chip Firing ◽  
Number Game

Abstract Jim Propp recently proposed a labeled version of chip-firing on a line and conjectured that this process is confluent from some initial configurations. This was proved by Hopkins–McConville–Propp. We reinterpret Propp’s labeled chip-firing moves in terms of root systems; a “central-firing” move consists of replacing a weight $\lambda$ by $\lambda +\alpha$ for any positive root $\alpha$ that is orthogonal to $\lambda$. We show that central-firing is always confluent from any initial weight after modding out by the Weyl group, giving a generalization of unlabeled chip-firing on a line to other types. For simply-laced root systems we describe this unlabeled chip-firing as a number game on the Dynkin diagram. We also offer a conjectural classification of when central-firing is confluent from the origin or a fundamental weight.

Distribution of secoiridoid glycosides in the root system of the medicinal plant Gentiana lutea L. subsp. aurantiaca

2017 ◽  
Author(s):  
Ó González-López ◽  
S Mayo ◽  
Á Rodríguez-González ◽  
G Carro-Huerga ◽  
V Suárez Villanueva ◽  
...  
Keyword(s):  
Medicinal Plant ◽  
Root System ◽  
Gentiana Lutea ◽  
Secoiridoid Glycosides

EFFECTS OF DECP PROCESSING ON THE ROOT SYSTEM OF COTTON

2019 ◽  
Vol 2 (1) ◽  
pp. 33-37
Author(s):  
Komiljon Komilov ◽  
◽  
Dilfuzakhon Komilova
Keyword(s):  
Root System

Global Genome Expression Analysis of Transcription Factors under PEG Osmotic Stress in Rice Root System

2009 ◽  
Vol 35 (6) ◽  
pp. 1030-1037 ◽  
Author(s):  
Ting-Chen MA ◽  
Rong-Jun CHEN ◽  
Rong-Rong YU ◽  
Han-Lai ZENG ◽  
Duan-Pin ZHANG
Keyword(s):  
Transcription Factors ◽  
Osmotic Stress ◽  
Root System ◽  
Expression Analysis ◽  
Rice Root ◽  
Genome Expression

Influence of Planting Methods on Root System Morphological and Physiologi-cal Characteristics of Super Rice under High-yielding Cultivation Condition

2012 ◽  
Vol 37 (12) ◽  
pp. 2208-2220
Author(s):  
Jie LI ◽  
Hong-Cheng ZHANG ◽  
Yong CHANG ◽  
Jin-Long GONG ◽  
Ya-Jie HU ◽  
...  
Keyword(s):  
Root System ◽  
Cultivation Condition ◽  
Planting Methods

Variability in Root System Characteristics of Kleingrass Seedlings 1

Crop Science ◽  
1980 ◽  
Vol 20 (3) ◽  
pp. 384-386 ◽  
Author(s):  
C. R. Rischler ◽  
R. L. Monk
Keyword(s):  
Root System ◽  
System Characteristics
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