11Bxx Sequences and sets
This subtopic studies sequences and sets of integers, emphasizing additive combinatorics, density questions, and the structure of arithmetic progressions and related patterns.
Specific topics
11B05 Density, gaps, topology
Overview
11B05 examines density, gaps, topology within sequences and sets. It emphasizes core definitions, typical theorem patterns, and computational viewpoints that are central in contemporary number theory.
Related Wikipedia Page
Density, gaps, topology (Wikipedia)
Useful Links
Key Ideas
- Precise formulations and standard examples for density, gaps, topology
- Proof techniques commonly used in elementary and analytic number theory
- Connections to algorithms, asymptotics, and structural invariants
Typical Uses
Used to choose effective proof strategies, compare competing formulations, and frame research-level questions in number theory and adjacent areas.
Applications
- Theoretical development in pure number theory
- Algorithm design and computational experimentation
- Cross-links to algebra, combinatorics, and cryptography
References
Recommended Textbooks
11B13 Additive bases, including sumsets
Overview
11B13 examines additive bases, including sumsets within sequences and sets. It emphasizes core definitions, typical theorem patterns, and computational viewpoints that are central in contemporary number theory.
Related Wikipedia Page
Additive bases, including sumsets (Wikipedia)
Useful Links
Key Ideas
- Precise formulations and standard examples for additive bases, including sumsets
- Proof techniques commonly used in elementary and analytic number theory
- Connections to algorithms, asymptotics, and structural invariants
Typical Uses
Used to choose effective proof strategies, compare competing formulations, and frame research-level questions in number theory and adjacent areas.
Applications
- Theoretical development in pure number theory
- Algorithm design and computational experimentation
- Cross-links to algebra, combinatorics, and cryptography
References
Recommended Textbooks
11B25 Arithmetic progressions
Overview
11B25 examines arithmetic progressions within sequences and sets. It emphasizes core definitions, typical theorem patterns, and computational viewpoints that are central in contemporary number theory.
Related Wikipedia Page
Arithmetic progressions (Wikipedia)
Useful Links
Key Ideas
- Precise formulations and standard examples for arithmetic progressions
- Proof techniques commonly used in elementary and analytic number theory
- Connections to algorithms, asymptotics, and structural invariants
Typical Uses
Used to choose effective proof strategies, compare competing formulations, and frame research-level questions in number theory and adjacent areas.
Applications
- Theoretical development in pure number theory
- Algorithm design and computational experimentation
- Cross-links to algebra, combinatorics, and cryptography
References
Recommended Textbooks
11B37 Recurrences
Overview
11B37 examines recurrences within sequences and sets. It emphasizes core definitions, typical theorem patterns, and computational viewpoints that are central in contemporary number theory.
Related Wikipedia Page
Recurrences (Wikipedia)
Useful Links
Key Ideas
- Precise formulations and standard examples for recurrences
- Proof techniques commonly used in elementary and analytic number theory
- Connections to algorithms, asymptotics, and structural invariants
Typical Uses
Used to choose effective proof strategies, compare competing formulations, and frame research-level questions in number theory and adjacent areas.
Applications
- Theoretical development in pure number theory
- Algorithm design and computational experimentation
- Cross-links to algebra, combinatorics, and cryptography
References
Recommended Textbooks
11B39 Fibonacci and Lucas numbers and polynomials
Overview
11B39 examines fibonacci and lucas numbers and polynomials within sequences and sets. It emphasizes core definitions, typical theorem patterns, and computational viewpoints that are central in contemporary number theory.
Related Wikipedia Page
Fibonacci and Lucas numbers and polynomials (Wikipedia)
Useful Links
Key Ideas
- Precise formulations and standard examples for fibonacci and lucas numbers and polynomials
- Proof techniques commonly used in elementary and analytic number theory
- Connections to algorithms, asymptotics, and structural invariants
Typical Uses
Used to choose effective proof strategies, compare competing formulations, and frame research-level questions in number theory and adjacent areas.
Applications
- Theoretical development in pure number theory
- Algorithm design and computational experimentation
- Cross-links to algebra, combinatorics, and cryptography
References
Recommended Textbooks
11B50 Sequences (mod $m$)
Overview
11B50 examines sequences (mod $m$) within sequences and sets. It emphasizes core definitions, typical theorem patterns, and computational viewpoints that are central in contemporary number theory.
Related Wikipedia Page
Sequences (mod $m$) (Wikipedia)
Useful Links
Key Ideas
- Precise formulations and standard examples for sequences (mod $m$)
- Proof techniques commonly used in elementary and analytic number theory
- Connections to algorithms, asymptotics, and structural invariants
Typical Uses
Used to choose effective proof strategies, compare competing formulations, and frame research-level questions in number theory and adjacent areas.
Applications
- Theoretical development in pure number theory
- Algorithm design and computational experimentation
- Cross-links to algebra, combinatorics, and cryptography
References
Recommended Textbooks
11B68 Bernoulli and Euler numbers and polynomials
Overview
11B68 examines bernoulli and euler numbers and polynomials within sequences and sets. It emphasizes core definitions, typical theorem patterns, and computational viewpoints that are central in contemporary number theory.
Related Wikipedia Page
Bernoulli and Euler numbers and polynomials (Wikipedia)
Useful Links
Key Ideas
- Precise formulations and standard examples for bernoulli and euler numbers and polynomials
- Proof techniques commonly used in elementary and analytic number theory
- Connections to algorithms, asymptotics, and structural invariants
Typical Uses
Used to choose effective proof strategies, compare competing formulations, and frame research-level questions in number theory and adjacent areas.
Applications
- Theoretical development in pure number theory
- Algorithm design and computational experimentation
- Cross-links to algebra, combinatorics, and cryptography
References
Recommended Textbooks
11B83 Special sequences and polynomials
Overview
11B83 examines special sequences and polynomials within sequences and sets. It emphasizes core definitions, typical theorem patterns, and computational viewpoints that are central in contemporary number theory.
Related Wikipedia Page
Special sequences and polynomials (Wikipedia)
Useful Links
Key Ideas
- Precise formulations and standard examples for special sequences and polynomials
- Proof techniques commonly used in elementary and analytic number theory
- Connections to algorithms, asymptotics, and structural invariants
Typical Uses
Used to choose effective proof strategies, compare competing formulations, and frame research-level questions in number theory and adjacent areas.
Applications
- Theoretical development in pure number theory
- Algorithm design and computational experimentation
- Cross-links to algebra, combinatorics, and cryptography
References
Recommended Textbooks