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

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Bullying

... basis of authority. The first to have the title of "Tyrant" was Pisistratus in 560 BC. In modern times Tyrant has come to mean a dictator who rules with ...

 
 
 
This page was created in 30.2 ms