![[50] Vertex Coverings by monochromatic Cycles and Trees.](http://s1.studyres.com/store/data/017263913_1-610cbf1ff480871337fed479f820c171-300x300.png)
[50] Vertex Coverings by monochromatic Cycles and Trees.
... the old c). Now we keep only those triangles which are colored with the color used most often, say red, we have at least cn 2 j(rt 3 ) = s red triangles, any two of them meeting in at most one vertex. Remove successively vertices and their incident red triangles if there are less than sjn red triang ...
... the old c). Now we keep only those triangles which are colored with the color used most often, say red, we have at least cn 2 j(rt 3 ) = s red triangles, any two of them meeting in at most one vertex. Remove successively vertices and their incident red triangles if there are less than sjn red triang ...
Induction and Recursion - Bryn Mawr Computer Science
... Definition 4 (Closed Form) If a sum with a variable number of terms is shown to be equal to a formula that does not contain either an ellipsis or a summation symbol, we say that it is written in closed form. Example 11 Consider the sequence 20 + 21 + · · · + 2n , is there any pattern w.r.t the value ...
... Definition 4 (Closed Form) If a sum with a variable number of terms is shown to be equal to a formula that does not contain either an ellipsis or a summation symbol, we say that it is written in closed form. Example 11 Consider the sequence 20 + 21 + · · · + 2n , is there any pattern w.r.t the value ...
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called ""Half Or Triple Plus One"", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.Paul Erdős said about the Collatz conjecture: ""Mathematics may not be ready for such problems."" He also offered $500 for its solution.