Synonyms for inclusion_exclusion_principle or Related words with inclusion_exclusion_principle
hahn_banach_theorem stone_weierstrass_theorem hensel_lemma cauchy_schwarz_inequality serre_duality cauchy_integral_formula cauchy_integral_theorem compactness_theorem fubini_theorem gauss_lemma poisson_summation_formula selberg_trace_formula chebyshev_inequality gröbner_basis radon_nikodym_theorem markov_inequality monotone_convergence_theorem sobolev_spaces plancherel_theorem banach_alaoglu_theorem hölder_inequality zorn_lemma mellin_transform hypergeometric_function binomial_theorem riemann_integral lagrange_interpolation realizability kuratowski riemann_roch_theorem generalized_riemann_hypothesis cobordism_theorem beltrami_equation reproducing_kernel_hilbert_space qr_decomposition modular_arithmetic symmetrization gödel_numbering euclidean_algorithm subadditive shapley_folkman_lemma chebotarev_density_theorem propositional_logic resolvent parseval_identity commutativity cauchy_theorem diagonalization poincaré_duality bézout_theoremExamples of "inclusion_exclusion_principle" |
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An extension of the addition law to any number of sets is the inclusion–exclusion principle. |
is called the flag "h"-vector of "P". By the inclusion–exclusion principle, |
The inclusion–exclusion principle is widely used and only a few of its applications can be mentioned here. |
Alon, Caro, Krasikov and Roditty showed that 1 + log("n") is sufficient, using a cleverly enhanced inclusion–exclusion principle. |
In mathematics, the Schuette–Nesbitt formula is a generalization of the inclusion–exclusion principle. It is named after Donald R. Schuette and Cecil J. Nesbitt. |
Let "A" denote the union formula_48 of the sets "A", ..., "A". To prove the inclusion–exclusion principle in general, we first verify the identity |
The inclusion–exclusion principle is sometimes attributed to da Silva, which was included in an 1854 publication. However, the result is normally attributed to Abraham de Moivre. |
In applications we pick "u" to get the best error term. In the sieve it represents the number of levels of the inclusion–exclusion principle. |
A different proof of the Sauer–Shelah lemma in its original form, by Péter Frankl and János Pach, is based on linear algebra and the inclusion–exclusion principle. |
The inclusion exclusion principle forms the basis of algorithms for a number of NP-hard graph partitioning problems, such as graph coloring. |
In terms of sieve theory the Brun sieve is of "combinatorial type"; that is, it derives from a careful use of the inclusion–exclusion principle. |
Boole's inequality is recovered by setting "k" = 1. When "k" = "n", then equality holds and the resulting identity is the inclusion–exclusion principle. |
Let "p", ..., "p" be the smallest "N" primes. Then by the inclusion–exclusion principle, the number of positive integers less than or equal to "x" that are divisible by one of those primes is |
For harder problems, it becomes increasingly important to find an efficient algorithm. For this problem, we can reduce 1000 operations to a handful by using the inclusion–exclusion principle and a closed-form summation formula. |
In terms of sieve theory the Turán sieve is of "combinatorial type": deriving from a rudimentary form of the inclusion–exclusion principle. The result gives an "upper bound" for the size of the sifted set. |
More generally, if "M" and "N" are subspaces of a larger space "X", then so are their union and intersection. In some cases, the Euler characteristic obeys a version of the inclusion–exclusion principle: |
In general, the inclusion–exclusion principle is false. A counterexample is given by taking "X" to be the real line, "M" a subset consisting of one point and "N" the complement of "M". |
It can be shown that the set of prices is coherent when they satisfy the probability axioms and related results such as the inclusion–exclusion principle (but not necessarily countable additivity). |
In combinatorics (combinatorial mathematics), the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as |
A well-known application of the inclusion–exclusion principle is to the combinatorial problem of counting all derangements of a finite set. A "derangement" of a set "A" is a bijection from "A" into itself that has no fixed points. Via the inclusion–exclusion principle one can show that if the cardinality of "A" is "n", then the number of derangements is ["n"! / "e"] where ["x"] denotes the nearest integer to "x"; a detailed proof is available here and also see the examples section above. |