Main Page | See live article | Alphabetical index Landau's function g(n) is defined for every positive integer n to be the largest order of an element of the symmetric group Sn. Equivalently, g(n) is the largest least common multiple of any partition of n. For instance, 5 = 2 + 3 and lcm(2,3) = 6. No other partition of 5 yields a bigger lcm, so g(5) = 6. An element of order 6 in the group S5 can be written in cycle notation as (1 2 3) (4 5). The integer sequence g(1) = 1, g(2) = 2, g(3) = 3, g(4) = 4, g(5) = 6, g(6) = 6, g(7) = 12, g(8) = 15, ... is A000793. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.