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In algebra and number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers less than n is one less than a multiple of n.
There also exists a Las Vegas construction that takes a random linear code and checks if this code has good Hamming distance, but this construction also has an exponential runtime. For sufficiently large non-prime q and for certain ranges of the variable δ, the Gilbert–Varshamov bound is surpassed by the Tsfasman–Vladut–Zink bound .
Wilson's academic interests lie in graph theory, particularly in colouring problems, e.g. the four colour problem, and algebraic properties of graphs.He also researches the history of mathematics, particularly British mathematics and mathematics in the 17th century and the period 1860 to 1940, and the history of graph theory and combinatorics.
Geometry Dash Lite is a free version of the game with advertisements and gameplay restrictions. Geometry Dash Lite includes only main levels 1-19, all tower levels, and a few selected levels that are either Featured, Daily, weekly or Event levels but does not offer the option to create levels or play most player-made levels. It also has a ...
The master theorem always yields asymptotically tight bounds to recurrences from divide and conquer algorithms that partition an input into smaller subproblems of equal sizes, solve the subproblems recursively, and then combine the subproblem solutions to give a solution to the original problem. The time for such an algorithm can be expressed ...
Hassler Whitney initiated the systematic study of immersions and regular homotopies in the 1940s, proving that for 2m < n + 1 every map f : M m → N n of an m-dimensional manifold to an n-dimensional manifold is homotopic to an immersion, and in fact to an embedding for 2m < n; these are the Whitney immersion theorem and Whitney embedding theorem.
The theorem generalizes the Riemann mapping theorem from conformal to quasiconformal homeomorphisms, and is stated as follows. Suppose that D is a simply connected domain in C that is not equal to C , and suppose that μ : D → C is Lebesgue measurable and satisfies ‖ μ ‖ ∞ < 1 {\displaystyle \|\mu \|_{\infty }<1} .
Algebraic geometry codes, often abbreviated AG codes, are a type of linear code that generalize Reed–Solomon codes. The Russian mathematician V. D. Goppa constructed these codes for the first time in 1982.