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If Kraft's inequality holds with strict inequality, the code has some redundancy. If Kraft's inequality holds with equality, the code in question is a complete code. [2] If Kraft's inequality does not hold, the code is not uniquely decodable. For every uniquely decodable code, there exists a prefix code with the same length distribution.
The acyclicity of G is an essential assumption in the Lindström–Gessel–Viennot lemma; it guarantees (in reasonable situations) that the sums (,) are well-defined, and it advects into the proof (if G is not acyclic, then f might transform a self-intersection of a path into an intersection of two distinct paths, which breaks the argument ...
In algebra, Gauss's lemma, [1] named after Carl Friedrich Gauss, is a theorem [note 1] about polynomials over the integers, or, more generally, over a unique factorization domain (that is, a ring that has a unique factorization property similar to the fundamental theorem of arithmetic).
The proof of the n th-power lemma uses the same ideas that were used in the proof of the quadratic lemma. The existence of the integers π(i) and b(i), and their uniqueness (mod m) and (mod n), respectively, come from the fact that Aμ is a representative set. Assume that π(i) = π(j) = p, i.e.
Eisenstein's proof of quadratic reciprocity is a simplification of Gauss's third proof. It is more geometrically intuitive and requires less technical manipulation. The point of departure is "Eisenstein's lemma", which states that for odd prime p and positive integer a not divisible by p,
When Kraft’s attendance was confirmed at the event, roasters were allegedly told not to make jokes about “happy endings” in relation to the Patriots owners. “When Tom checked Jeff Ross, I ...
Kraft issued an apology to a TikToker who said she was missing cheese sauce in her gluten-free mac and cheese. Boxes of gluten-free Kraft Mac & Cheese are missing sauce packets. It took 1 woman's ...
In ergodic theory, Kac's lemma, demonstrated by mathematician Mark Kac in 1947, [1] is a lemma stating that in a measure space the orbit of almost all the points contained in a set of such space, whose measure is (), return to within an average time inversely proportional to ().