Chip Firing Games and Riemann-Roch Properties for Directed Graphs

The following presents a brief introduction to tropical geometry, especially tropical curves, and explains a connection to graph theory. We also give a brief summary of the Riemann-Roch property for graphs, established by Baker and Norine (2007), as well as the tools used in their proof. Various gen...

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Main Author:	Gaslowitz, Joshua Z
Format:	Others
Published:	Scholarship @ Claremont 2013
Subjects:	Algebraic Geometry Discrete Mathematics and Combinatorics
Online Access:	http://scholarship.claremont.edu/hmc_theses/42 http://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1051&context=hmc_theses

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spelling	ndltd-CLAREMONT-oai-scholarship.claremont.edu-hmc_theses-10512013-12-22T15:20:53Z Chip Firing Games and Riemann-Roch Properties for Directed Graphs Gaslowitz, Joshua Z The following presents a brief introduction to tropical geometry, especially tropical curves, and explains a connection to graph theory. We also give a brief summary of the Riemann-Roch property for graphs, established by Baker and Norine (2007), as well as the tools used in their proof. Various generalizations are described, including a more thorough description of the extension to strongly connected directed graphs by Asadi and Backman (2011). Building from their constructions, an algorithm to determine if a directed graph has Row Riemann-Roch Property is given and thoroughly explained. 2013-05-01T07:00:00Z text application/pdf http://scholarship.claremont.edu/hmc_theses/42 http://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1051&context=hmc_theses J. Zachary Gaslowitz HMC Senior Theses Scholarship @ Claremont Algebraic Geometry Discrete Mathematics and Combinatorics
collection	NDLTD
format	Others
sources	NDLTD
topic	Algebraic Geometry Discrete Mathematics and Combinatorics
spellingShingle	Algebraic Geometry Discrete Mathematics and Combinatorics Gaslowitz, Joshua Z Chip Firing Games and Riemann-Roch Properties for Directed Graphs
description	The following presents a brief introduction to tropical geometry, especially tropical curves, and explains a connection to graph theory. We also give a brief summary of the Riemann-Roch property for graphs, established by Baker and Norine (2007), as well as the tools used in their proof. Various generalizations are described, including a more thorough description of the extension to strongly connected directed graphs by Asadi and Backman (2011). Building from their constructions, an algorithm to determine if a directed graph has Row Riemann-Roch Property is given and thoroughly explained.
author	Gaslowitz, Joshua Z
author_facet	Gaslowitz, Joshua Z
author_sort	Gaslowitz, Joshua Z
title	Chip Firing Games and Riemann-Roch Properties for Directed Graphs
title_short	Chip Firing Games and Riemann-Roch Properties for Directed Graphs
title_full	Chip Firing Games and Riemann-Roch Properties for Directed Graphs
title_fullStr	Chip Firing Games and Riemann-Roch Properties for Directed Graphs
title_full_unstemmed	Chip Firing Games and Riemann-Roch Properties for Directed Graphs
title_sort	chip firing games and riemann-roch properties for directed graphs
publisher	Scholarship @ Claremont
publishDate	2013
url	http://scholarship.claremont.edu/hmc_theses/42 http://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1051&context=hmc_theses
work_keys_str_mv	AT gaslowitzjoshuaz chipfiringgamesandriemannrochpropertiesfordirectedgraphs
_version_	1716621629168025600

Chip Firing Games and Riemann-Roch Properties for Directed Graphs

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