No doubts, the inclusion-exclusion principleinclusion-exclusion principle generates most common type of formulae used in enumerative combinatorics. ExamplesExamples include explicit formulae for derangements, Striling numbers, rook polynomials, Euler's totient function, and so on.
$$\left\lvert \bigcup_{i=1}^n A_i \right\rvert = \sum_{\emptyset\ne J\subseteq\{1,2,\dots,n\}} (-1)^{|J|-1} \left\lvert \bigcap_{j\in J}^n A_j \right\rvert$$
No doubts, the inclusion-exclusion principle generates most common type of formulae used in enumerative combinatorics. Examples include explicit formulae for derangements, Striling numbers, rook polynomials, Euler's totient function, and so on.
No doubts, the inclusion-exclusion principle generates most common type of formulae used in enumerative combinatorics. Examples include explicit formulae for derangements, Striling numbers, rook polynomials, Euler's totient function, and so on.
$$\left\lvert \bigcup_{i=1}^n A_i \right\rvert = \sum_{\emptyset\ne J\subseteq\{1,2,\dots,n\}} (-1)^{|J|-1} \left\lvert \bigcap_{j\in J}^n A_j \right\rvert$$
No doubts, the inclusion-exclusion principle generates most common type of formulae used in enumerative combinatorics. Examples include explicit formulae for derangements, Striling numbers, rook polynomials, Euler's totient function, and so on.
No doubts, the inclusion-exclusion principle generates most common type of formulae used in enumerative combinatorics. Examples include explicit formulae for derangements, Striling numbers, rook polynomials, Euler's totient function, and so on.
No doubts, the inclusion-exclusion principle generates most common type of formulae used in enumerative combinatorics. Examples include explicit formulae for derangements, Striling numbers, rook polynomials, Euler's totient function, and so on.
