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  2. Inclusion–exclusion principle - Wikipedia

    en.wikipedia.org/wiki/Inclusionexclusion...

    Inclusionexclusion principle. In combinatorics, a branch of mathematics, the inclusionexclusion 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. where A and B are two finite sets and | S | indicates the cardinality of a ...

  3. Combinatorial principles - Wikipedia

    en.wikipedia.org/wiki/Combinatorial_principles

    Combinatorial principles. In proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used. The rule of sum, rule of product, and inclusionexclusion principle are often used for enumerative purposes. Bijective proofs are utilized to demonstrate that two sets have the same ...

  4. Euler characteristic - Wikipedia

    en.wikipedia.org/wiki/Euler_characteristic

    In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space 's shape or structure regardless of the way it is bent. It is commonly denoted by (Greek lower-case ...

  5. Assimilation and contrast effects - Wikipedia

    en.wikipedia.org/wiki/Assimilation_and_contrast...

    The inclusion/exclusion model [ edit ] A more specific model to predict assimilation and contrast effects with differences in categorizing information is the inclusion/exclusion model developed 1992 by Norbert Schwarz and Herbert Bless.< [ 7 ] It explains the mechanism through which effects occur. [ 8 ]

  6. Derangement - Wikipedia

    en.wikipedia.org/wiki/Derangement

    In combinatorial mathematics, a derangement is a permutation of the elements of a set in which no element appears in its original position. In other words, a derangement is a permutation that has no fixed points. The number of derangements of a set of size n is known as the subfactorial of n or the n- th derangement number or n- th de Montmort ...

  7. Sieve theory - Wikipedia

    en.wikipedia.org/wiki/Sieve_theory

    Sieve theory is a set of general techniques in number theory, designed to count, or more realistically to estimate the size of, sifted sets of integers. The prototypical example of a sifted set is the set of prime numbers up to some prescribed limit X. Correspondingly, the prototypical example of a sieve is the sieve of Eratosthenes, or the ...

  8. Möbius inversion formula - Wikipedia

    en.wikipedia.org/wiki/Möbius_inversion_formula

    A simple example of the use of this formula is counting the number of reduced fractions 0 < ⁠ a / b ⁠ < 1, where a and b are coprime and b ≤ n. If we let f ( n ) be this number, then g ( n ) is the total number of fractions 0 < ⁠ a / b ⁠ < 1 with b ≤ n , where a and b are not necessarily coprime.

  9. Opinion - Taiwan’s exclusion from the UN defies inclusion and ...

    www.aol.com/opinion-taiwan-exclusion-un-defies...

    Taiwan's exclusion from the UN is being challenged by the global community due to China's undue influence and expansionist ambitions, as well as its false claims to Taiwan's territory, and the ...