Search the Kids Internet
Encyclopedia > Landau's function
Article Content
Landau's function
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 largests 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 (http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A000793).
All Wikipedia text is available under the terms of the GNU Free Documentation License
|
Search Encyclopedia
|
Featured Article
|