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A137840
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Number of distinct n-ary operators in a quaternary logic.
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4
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4, 256, 4294967296, 340282366920938463463374607431768211456, 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096
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OFFSET
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0,1
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COMMENTS
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The total number of n-ary operators in a k-valued logic is T = k^(k^n), i.e. if S is a set of k elements, there are T ways of mapping an ordered subset of n elements taken from S to an element of S. Some operators are "degenerate": the operator has arity p, if only p of the n input values influence the output. Therefore the set of operators can be partitioned into n+1 disjoint subsets representing arities from 0 to n.
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LINKS
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FORMULA
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a(n) = 4^(4^n).
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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