52Cxx Discrete geometry
This subtopic introduces the core ideas in discrete geometry, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
Specific topics
52C05 Lattices and convex bodies in $2$ dimensions
Overview
Lattices and convex bodies in $2$ dimensions. This topic studies finite and discrete geometric configurations such as packings, tilings, and incidence arrangements.
Related Wikipedia Page
Wikipedia: Discrete geometry
Useful Links
Key Ideas
- packings, coverings, and tilings
- incidence and extremal configurations
- algorithmic and combinatorial methods
Typical Uses
Used for finite geometric structure, optimization over configurations, and algorithm design with geometric data.
Applications
- Coding theory
- Computational geometry
- Materials and packing models
References
Recommended Textbooks
52C07 Lattices and convex bodies in $n$ dimensions
Overview
Lattices and convex bodies in $n$ dimensions. This topic studies finite and discrete geometric configurations such as packings, tilings, and incidence arrangements.
Related Wikipedia Page
Wikipedia: Discrete geometry
Useful Links
Key Ideas
- packings, coverings, and tilings
- incidence and extremal configurations
- algorithmic and combinatorial methods
Typical Uses
Used for finite geometric structure, optimization over configurations, and algorithm design with geometric data.
Applications
- Coding theory
- Computational geometry
- Materials and packing models
References
Recommended Textbooks
52C10 Erd\H{o}s problems and related topics of discrete geometry
Overview
Erd\H{o}s problems and related topics of discrete geometry. This topic studies finite and discrete geometric configurations such as packings, tilings, and incidence arrangements.
Related Wikipedia Page
Wikipedia: Discrete geometry
Useful Links
Key Ideas
- packings, coverings, and tilings
- incidence and extremal configurations
- algorithmic and combinatorial methods
Typical Uses
Used for finite geometric structure, optimization over configurations, and algorithm design with geometric data.
Applications
- Coding theory
- Computational geometry
- Materials and packing models
References
Recommended Textbooks
52C15 Packing and covering in $2$ dimensions
Overview
Packing and covering in $2$ dimensions. This topic studies finite and discrete geometric configurations such as packings, tilings, and incidence arrangements.
Related Wikipedia Page
Wikipedia: Discrete geometry
Useful Links
Key Ideas
- packings, coverings, and tilings
- incidence and extremal configurations
- algorithmic and combinatorial methods
Typical Uses
Used for finite geometric structure, optimization over configurations, and algorithm design with geometric data.
Applications
- Coding theory
- Computational geometry
- Materials and packing models
References
Recommended Textbooks
52C17 Packing and covering in $n$ dimensions
Overview
Packing and covering in $n$ dimensions. This topic studies finite and discrete geometric configurations such as packings, tilings, and incidence arrangements.
Related Wikipedia Page
Wikipedia: Discrete geometry
Useful Links
Key Ideas
- packings, coverings, and tilings
- incidence and extremal configurations
- algorithmic and combinatorial methods
Typical Uses
Used for finite geometric structure, optimization over configurations, and algorithm design with geometric data.
Applications
- Coding theory
- Computational geometry
- Materials and packing models
References
Recommended Textbooks
52C20 Tilings in $2$ dimensions
Overview
Tilings in $2$ dimensions. This topic studies finite and discrete geometric configurations such as packings, tilings, and incidence arrangements.
Related Wikipedia Page
Wikipedia: Discrete geometry
Useful Links
Key Ideas
- packings, coverings, and tilings
- incidence and extremal configurations
- algorithmic and combinatorial methods
Typical Uses
Used for finite geometric structure, optimization over configurations, and algorithm design with geometric data.
Applications
- Coding theory
- Computational geometry
- Materials and packing models
References
Recommended Textbooks
52C22 Tilings in $n$ dimensions
Overview
Tilings in $n$ dimensions. This topic studies finite and discrete geometric configurations such as packings, tilings, and incidence arrangements.
Related Wikipedia Page
Wikipedia: Discrete geometry
Useful Links
Key Ideas
- packings, coverings, and tilings
- incidence and extremal configurations
- algorithmic and combinatorial methods
Typical Uses
Used for finite geometric structure, optimization over configurations, and algorithm design with geometric data.
Applications
- Coding theory
- Computational geometry
- Materials and packing models
References
Recommended Textbooks
52C23 Quasicrystals and aperiodic tilings in discrete geometry
Overview
Quasicrystals and aperiodic tilings in discrete geometry. This topic studies finite and discrete geometric configurations such as packings, tilings, and incidence arrangements.
Related Wikipedia Page
Wikipedia: Discrete geometry
Useful Links
Key Ideas
- packings, coverings, and tilings
- incidence and extremal configurations
- algorithmic and combinatorial methods
Typical Uses
Used for finite geometric structure, optimization over configurations, and algorithm design with geometric data.
Applications
- Coding theory
- Computational geometry
- Materials and packing models
References
Recommended Textbooks
52C25 Rigidity and flexibility of structures
Overview
Rigidity and flexibility of structures. This topic studies finite and discrete geometric configurations such as packings, tilings, and incidence arrangements.
Related Wikipedia Page
Wikipedia: Discrete geometry
Useful Links
Key Ideas
- packings, coverings, and tilings
- incidence and extremal configurations
- algorithmic and combinatorial methods
Typical Uses
Used for finite geometric structure, optimization over configurations, and algorithm design with geometric data.
Applications
- Coding theory
- Computational geometry
- Materials and packing models
References
Recommended Textbooks
52C26 Circle packings and discrete conformal geometry
Overview
Circle packings and discrete conformal geometry. This topic studies finite and discrete geometric configurations such as packings, tilings, and incidence arrangements.
Related Wikipedia Page
Wikipedia: Discrete geometry
Useful Links
Key Ideas
- packings, coverings, and tilings
- incidence and extremal configurations
- algorithmic and combinatorial methods
Typical Uses
Used for finite geometric structure, optimization over configurations, and algorithm design with geometric data.
Applications
- Coding theory
- Computational geometry
- Materials and packing models
References
Recommended Textbooks
52C30 Planar arrangements of lines and pseudo-lines
Overview
Planar arrangements of lines and pseudo-lines. This topic studies finite and discrete geometric configurations such as packings, tilings, and incidence arrangements.
Related Wikipedia Page
Wikipedia: Discrete geometry
Useful Links
Key Ideas
- packings, coverings, and tilings
- incidence and extremal configurations
- algorithmic and combinatorial methods
Typical Uses
Used for finite geometric structure, optimization over configurations, and algorithm design with geometric data.
Applications
- Coding theory
- Computational geometry
- Materials and packing models
References
Recommended Textbooks
52C35 Arrangements of points, flats, hyperplanes
Overview
Arrangements of points, flats, hyperplanes. This topic studies finite and discrete geometric configurations such as packings, tilings, and incidence arrangements.
Related Wikipedia Page
Wikipedia: Discrete geometry
Useful Links
Key Ideas
- packings, coverings, and tilings
- incidence and extremal configurations
- algorithmic and combinatorial methods
Typical Uses
Used for finite geometric structure, optimization over configurations, and algorithm design with geometric data.
Applications
- Coding theory
- Computational geometry
- Materials and packing models
References
Recommended Textbooks
52C40 Oriented matroids in discrete geometry
Overview
Oriented matroids in discrete geometry. This topic studies finite and discrete geometric configurations such as packings, tilings, and incidence arrangements.
Related Wikipedia Page
Wikipedia: Discrete geometry
Useful Links
Key Ideas
- packings, coverings, and tilings
- incidence and extremal configurations
- algorithmic and combinatorial methods
Typical Uses
Used for finite geometric structure, optimization over configurations, and algorithm design with geometric data.
Applications
- Coding theory
- Computational geometry
- Materials and packing models
References
Recommended Textbooks
52C45 Combinatorial complexity of geometric structures
Overview
Combinatorial complexity of geometric structures. This topic studies finite and discrete geometric configurations such as packings, tilings, and incidence arrangements.
Related Wikipedia Page
Wikipedia: Discrete geometry
Useful Links
Key Ideas
- packings, coverings, and tilings
- incidence and extremal configurations
- algorithmic and combinatorial methods
Typical Uses
Used for finite geometric structure, optimization over configurations, and algorithm design with geometric data.
Applications
- Coding theory
- Computational geometry
- Materials and packing models
References
Recommended Textbooks