inclusion-exclusion principle


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inclusion-exclusion principle

[¦in‚klü·zhən ′eks‚klü·zhən ‚prin·sə·pəl]
(mathematics)
The principle that, if A and B are finite sets, the number of elements in the union of A and B can be obtained by adding the number of elements in A to the number of elements in B, and then subtracting from this sum the number of elements in the intersection of A and B.
References in periodicals archive ?
They cover initial encounters with combinatorial reasoning; selections, arrangements, and distributions; binomial series and generating functions; alternating sums, the inclusion-exclusion principle, rook polynomials, and Fibonacci Nim; recurrence relations; special numbers; linear spaces and recurrence sequences; and counting with symmetries.
They explain such topics as combinatorics is, permutations and combinations, the inclusion-exclusion principle, generating functions and recurrence relations, trees, group actions, and Dirichlet's pigeonhole principle.
The application of the inclusion-exclusion principle to word counting due to Goulden and Jackson (1979, 1983) is used to derive the result.
We describe and prove our results in Section 3 using the inclusion-exclusion principle.
This multiple counting is eliminated by use of the inclusion-exclusion principle (see among others [GJ83], [Szp01], and [FS07, 111.