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This last example shows that a set that is intuitively "nearly sorted" can still have a quadratic number of inversions. The inversion number is the number of crossings in the arrow diagram of the permutation, [ 6 ] the permutation's Kendall tau distance from the identity permutation, and the sum of each of the inversion related vectors defined ...
Type inference and type checking for the second-order lambda calculus (or equivalent). [1] Determining whether a first-order sentence in the logic of graphs can be realized by a finite undirected graph. [2] Trakhtenbrot's theorem - Finite satisfiability is undecidable. Satisfiability of first order Horn clauses.
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field.
This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...
The congruence relation, modulo m, partitions the set of integers into m congruence classes. Operations of addition and multiplication can be defined on these m objects in the following way: To either add or multiply two congruence classes, first pick a representative (in any way) from each class, then perform the usual operation for integers on the two representatives and finally take the ...
For example, to add 3 and 4 together, the expression is 3 4 + rather than 3 + 4. The conventional notation expression 3 − 4 + 5 becomes 3 (enter) 4 − 5 + in reverse Polish notation: 4 is first subtracted from 3, then 5 is added to it. The concept of a stack, a last-in/first-out construct, is integral to the left-to-right evaluation of RPN.
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