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## concatenation

concatenation The operation of joining two strings to form a longer string. The concatenation of the strings u = a1,…,am and v = b1,…,bn

is the following string of length m + n: a1,…,amb1,…,bn

Common notations for referring to it include uv and u<>v, but others are also used.

The term concatenation is also generalized to an operation on sets of strings (i.e. formal languages). Let K and L be two sets of strings. Then they can be combined into the following set by concatenating strings from K with strings from L in all possible ways: {uv | u K, vL}

This set is usually written KL. The phrase language concatenation is sometimes used to distinguish this from simple concatenation of strings. Both string concatenation and language concatenation gives rise to monoids, the identity elements being Λ and {Λ} respectively (where Λ is the empty string).

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## concatenation

concatenation. Union by chaining parts together, as with separate architectural elements in a long façade (each with its own roof and separate composition), the fronts being brought forward or recessed, also called staccato composition. Concatenated façades were favoured by William Kent and other Palladians for articulation. See also additive.

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# Concatenation

a chain; a sequence of things or sounds dependent on each other. See also catena, chain.

Examples: concatenation of bungles and contradictions, 1880; of causes and effects, 1753; of explosions; of felicity, 1622; of ideas, 1867; of orgiasts; of straight lines, 1845.