Mathematics of Chip-Firing
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portes grátis
Mathematics of Chip-Firing
Klivans, Caroline J.
Taylor & Francis Ltd
11/2018
296
Dura
Inglês
9781138070820
15 a 20 dias
698
Descrição não disponível.
Introduction
A brief introduction. Origins/History.
Chip-firing on Finite Graphs
The chip-firing process. Confluence. Stabilization. Toppling time. Stabilization with a sink. Long-term stable configurations. The sandpile Markov chain.
Spanning Trees
Spanning trees. Statistics on Trees. Merino's Theorem. Cori-Le Borgne bijection. Acyclic orientations. Parking functions. Dominoes. Avalanche polynomials.
Sandpile Groups
Toppling dynamics. Group of chip-firing equivalence. Identity. Combinatorial invariance. Sandpile groups and invariant factors. Discriminant groups. Sandpile torsors.
Pattern Formation
Compelling visualizations. Infinite graphs. The one-dimensional grid. Labeled chip-firing. Two and more dimensional grids. Other lattices. The identity element.
Avalanche Finite Systems
M-matrices. Chip-firing on M-matrices. Stability. Burning. Directed graphs. Cartan matrices as M-matrices. M-pairings.
Higher Dimensions
An illustrative example. Cell complexes. Combinatorial Laplacians. Chip-firing in higher dimensions. The sandpile group. Higher-dimensional trees. Sandpile groups. Cuts and flows. Stability.
Divisors
Divisors on curves. The Picard group and Abel-Jacobi theory. Riemann-Roch Theorems. Torelli's Theorem. The Pic^g (G) torus. Metric graphs and tropical geometry. Arithmetic geometry. Arithmetical graphs. Riemann-Roch for lattices. Two variable zeta-functions. Enumerating arithmetical structures.
Ideals
Ideals. Toppling ideals. Tree ideals. Resolutions. Critical ideals. Riemann-Roch for monomial ideals.
A brief introduction. Origins/History.
Chip-firing on Finite Graphs
The chip-firing process. Confluence. Stabilization. Toppling time. Stabilization with a sink. Long-term stable configurations. The sandpile Markov chain.
Spanning Trees
Spanning trees. Statistics on Trees. Merino's Theorem. Cori-Le Borgne bijection. Acyclic orientations. Parking functions. Dominoes. Avalanche polynomials.
Sandpile Groups
Toppling dynamics. Group of chip-firing equivalence. Identity. Combinatorial invariance. Sandpile groups and invariant factors. Discriminant groups. Sandpile torsors.
Pattern Formation
Compelling visualizations. Infinite graphs. The one-dimensional grid. Labeled chip-firing. Two and more dimensional grids. Other lattices. The identity element.
Avalanche Finite Systems
M-matrices. Chip-firing on M-matrices. Stability. Burning. Directed graphs. Cartan matrices as M-matrices. M-pairings.
Higher Dimensions
An illustrative example. Cell complexes. Combinatorial Laplacians. Chip-firing in higher dimensions. The sandpile group. Higher-dimensional trees. Sandpile groups. Cuts and flows. Stability.
Divisors
Divisors on curves. The Picard group and Abel-Jacobi theory. Riemann-Roch Theorems. Torelli's Theorem. The Pic^g (G) torus. Metric graphs and tropical geometry. Arithmetic geometry. Arithmetical graphs. Riemann-Roch for lattices. Two variable zeta-functions. Enumerating arithmetical structures.
Ideals
Ideals. Toppling ideals. Tree ideals. Resolutions. Critical ideals. Riemann-Roch for monomial ideals.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
Finite Root System;Chip-firing;Superstable Configurations;Combinatorics;Tutte Polynomial;Networks;Cellular Automaton;Discrete dynamical systems;Critical Configurations;Avalanching;Discriminant Groups;The Abelian Sandpile Model;Graph Laplacian;Sink Vertex;Smith Normal Form;Critical Polynomial;Finite Simple Graph;Clifford's Theorem;Generalized Laplacian;Riemann Roch Theorem;Graphical Matroid;Canonical Divisor;Matrix Tree Theorem;Monomial Ideal;Effective Divisor;Finite Abelian Group;Arithmetical Graph;Standard Monomials;Break Configuration;Hyperplane Arrangement;Torsor Structure
Introduction
A brief introduction. Origins/History.
Chip-firing on Finite Graphs
The chip-firing process. Confluence. Stabilization. Toppling time. Stabilization with a sink. Long-term stable configurations. The sandpile Markov chain.
Spanning Trees
Spanning trees. Statistics on Trees. Merino's Theorem. Cori-Le Borgne bijection. Acyclic orientations. Parking functions. Dominoes. Avalanche polynomials.
Sandpile Groups
Toppling dynamics. Group of chip-firing equivalence. Identity. Combinatorial invariance. Sandpile groups and invariant factors. Discriminant groups. Sandpile torsors.
Pattern Formation
Compelling visualizations. Infinite graphs. The one-dimensional grid. Labeled chip-firing. Two and more dimensional grids. Other lattices. The identity element.
Avalanche Finite Systems
M-matrices. Chip-firing on M-matrices. Stability. Burning. Directed graphs. Cartan matrices as M-matrices. M-pairings.
Higher Dimensions
An illustrative example. Cell complexes. Combinatorial Laplacians. Chip-firing in higher dimensions. The sandpile group. Higher-dimensional trees. Sandpile groups. Cuts and flows. Stability.
Divisors
Divisors on curves. The Picard group and Abel-Jacobi theory. Riemann-Roch Theorems. Torelli's Theorem. The Pic^g (G) torus. Metric graphs and tropical geometry. Arithmetic geometry. Arithmetical graphs. Riemann-Roch for lattices. Two variable zeta-functions. Enumerating arithmetical structures.
Ideals
Ideals. Toppling ideals. Tree ideals. Resolutions. Critical ideals. Riemann-Roch for monomial ideals.
A brief introduction. Origins/History.
Chip-firing on Finite Graphs
The chip-firing process. Confluence. Stabilization. Toppling time. Stabilization with a sink. Long-term stable configurations. The sandpile Markov chain.
Spanning Trees
Spanning trees. Statistics on Trees. Merino's Theorem. Cori-Le Borgne bijection. Acyclic orientations. Parking functions. Dominoes. Avalanche polynomials.
Sandpile Groups
Toppling dynamics. Group of chip-firing equivalence. Identity. Combinatorial invariance. Sandpile groups and invariant factors. Discriminant groups. Sandpile torsors.
Pattern Formation
Compelling visualizations. Infinite graphs. The one-dimensional grid. Labeled chip-firing. Two and more dimensional grids. Other lattices. The identity element.
Avalanche Finite Systems
M-matrices. Chip-firing on M-matrices. Stability. Burning. Directed graphs. Cartan matrices as M-matrices. M-pairings.
Higher Dimensions
An illustrative example. Cell complexes. Combinatorial Laplacians. Chip-firing in higher dimensions. The sandpile group. Higher-dimensional trees. Sandpile groups. Cuts and flows. Stability.
Divisors
Divisors on curves. The Picard group and Abel-Jacobi theory. Riemann-Roch Theorems. Torelli's Theorem. The Pic^g (G) torus. Metric graphs and tropical geometry. Arithmetic geometry. Arithmetical graphs. Riemann-Roch for lattices. Two variable zeta-functions. Enumerating arithmetical structures.
Ideals
Ideals. Toppling ideals. Tree ideals. Resolutions. Critical ideals. Riemann-Roch for monomial ideals.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
Finite Root System;Chip-firing;Superstable Configurations;Combinatorics;Tutte Polynomial;Networks;Cellular Automaton;Discrete dynamical systems;Critical Configurations;Avalanching;Discriminant Groups;The Abelian Sandpile Model;Graph Laplacian;Sink Vertex;Smith Normal Form;Critical Polynomial;Finite Simple Graph;Clifford's Theorem;Generalized Laplacian;Riemann Roch Theorem;Graphical Matroid;Canonical Divisor;Matrix Tree Theorem;Monomial Ideal;Effective Divisor;Finite Abelian Group;Arithmetical Graph;Standard Monomials;Break Configuration;Hyperplane Arrangement;Torsor Structure
