Combinatorics Basic counting Concept
Binomial coefficient
Summary
The binomial coefficient is the number of ways to choose elements from an -element set. These numbers are the coefficients in the expansion of . The node binomial coefficient gives the precise definition.
Where this leads
20 pages build on this one.
- g-theorem
- WZ theory
- Grünwald–Letnikov derivative
- Chu–Vandermonde identity
- Macdonald constant term conjecture
- Simple random sample
- f-vector and h-vector
- Upper bound theorem
- Hahn polynomials
- LYM inequality
- Charlier polynomials
- Erdős–Ko–Rado theorem
- Kruskal–Katona theorem
- Erdős–Rényi model
- Dyson conjecture
- Wilf–Zeilberger pair
- Newton–Gregory forward formula
- Dixon's identity
- Gaussian binomial coefficient
- Sauer–Shelah lemma
Further reading
- Web https://en.wikipedia.org/wiki/Binomial_coefficient, Definition and interpretations
About this page
| Tag | 0GBZM0MT0F |
|---|---|
| URI | m2://0GBZM0MT0F |
| Kind | concept |
| Writing | W1 stated |
| MSC | 05A10 |
| Specializes | Multinomial coefficient |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
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What links here
Definitions
Special cases
Used by
- g-theorem
- WZ theory
- Grünwald–Letnikov derivative
- Chu–Vandermonde identity
- Macdonald constant term conjecture
- Simple random sample
- f-vector and h-vector
- Hahn polynomials
- LYM inequality
- Charlier polynomials
- Erdős–Ko–Rado theorem
- Kruskal–Katona theorem
- Erdős–Rényi model
- Dyson conjecture
- Wilf–Zeilberger pair
- Newton–Gregory forward formula
- Dixon's identity
- Gaussian binomial coefficient
- Sauer–Shelah lemma