Sandpile models and lattices: a comprehensive survey
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Title: Sandpile models and lattices: a comprehensive survey

Section 1: Introduction
Description 1: Introduce the fundamental concepts and significance of sandpile models and lattices.

Section 2: Historical Context
Description 2: Provide a historical background on the development and study of sandpile models and lattices.

Section 3: Young Lattices
Description 3: Discuss the Young lattices, their properties, and their relation to sandpile models.

Section 4: Brylawski Model
Description 4: Explain the Brylawski model, its evolution rules, and its configuration space.

Section 5: Sand Pile Model (SPM)
Description 5: Describe the Sand Pile Model, its rules, and its significance in studying Self-Organized Criticality (SOC).

Section 6: Ice Pile Model and Generalizations
Description 6: Review various modifications and generalizations of sandpile models, including the Ice Pile Model.

Section 7: Abelian Sandpile Model (ASM)
Description 7: Analyze the Abelian Sandpile Model and its algebraic properties.

Section 8: Chip Firing Games (CFG)
Description 8: Outline the fundamentals of Chip Firing Games and how they encompass various other models.

Section 9: The Simple Chip Firing Game
Description 9: Introduce and discuss the concept of simple CFGs and their properties.

Section 10: Conclusion and Perspectives
Description 10: Summarize the findings and discuss future research directions in the study of sandpile models and lattices.

Section 11: Different Classes of Lattices
Description 11: Explore different classes of lattices and their relations to CFGs and other models.

Section 12: Generalizations of the Models
Description 12: Discuss potential generalizations of sandpile models and CFGs.

Section 13: Infinite Extensions
Description 13: Explain the possibility and implications of infinite extensions of these models.

Section 14: Algebraic Properties
Description 14: Investigate the algebraic properties of configurations within these models.

Section 15: Tilings Problems
Description 15: Describe how discrete dynamical models apply to tiling problems and their resulting lattice structures.