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The ordered Bell numbers were studied in the 19th century by Arthur Cayleyand William Allen Whitworth. They are named after Eric Temple Bell, who wrote about the Bell numbers, which count the partitions of a set; the ordered Bell numbers count partitions that have been equipped with a total order.
The total number of partitions of an n-element set is the Bell number B n. The first several Bell numbers are B 0 = 1, B 1 = 1, B 2 = 2, B 3 = 5, B 4 = 15, B 5 = 52, and B 6 = 203 (sequence A000110 in the OEIS). Bell numbers satisfy the recursion + = = and have the exponential generating function
Bell polynomials. In combinatorial mathematics, the Bell polynomials, named in honor of Eric Temple Bell, are used in the study of set partitions. They are related to Stirling and Bell numbers. They also occur in many applications, such as in Faà di Bruno's formula.
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation. A simpler example is equality. Any number is equal to itself (reflexive). If , then (symmetric).
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Dobiński's formula. In combinatorial mathematics, Dobiński's formula[1] states that the n -th Bell number Bn (i.e., the number of partitions of a set of size n) equals. where denotes Euler's number. The formula is named after G. Dobiński, who published it in 1877.
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement. "Local" here refers to the principle of locality, the idea that a particle can only be influenced ...
Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks. [ 1 ][ 2 ] The best known example of quantum cryptography is quantum key distribution, which offers an information-theoretically secure solution to the key exchange problem.