Abelian Sandpile Model Of A Directed Multi-graph
Abstract
In this project, we study the combinatorics, algebraic and algebraic geometry of an Abelian
Sandpile Model (ASM). We aim to explore the Algebraic properties of the Abelian Sandpile
Model (ASM). We also aim to study the algebraic geometry of the Abelian Sandpile Model
(ASM).
In this model, we consider a directed multi graph with a sink vertex which is accessible
from every other vertex and associates with it a commutative monoidM, a commutative
semigroupS and a commutative GroupG which finally turns out to be the sandpile monoid,
sandpile semigroup and sandpile group respectively. We observe that the sandpile group is
the unique minimal ideal of the sandpile monoid [21]. We study the combinatorial structure
of our model and the connections between the algebraic structure of the sandpile monoid,
the sandpile semigroup and the sandpile group.
Citation
Master of Science in Pure Mathematics, University of Nairobi, 2014Publisher
University of Nairobi