Landau's function: Difference between revisions

Latest revision as of 21:00, 30 April 2009

Let $n$ be a nonnegative integer. The Landau's function of $n$ is defined in the following equivalent ways:

The maximum possible value for the least common multiple of the parts in an unordered integer partition of $n$ .
The maximum of the orders of all elements in the symmetric group of degree $n$ .

The value at $n=0$ is defined to be $1$ .

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A000793

The values of Landau's function for $n=0,1,2,3,4,5,6,7$ is $1,1,2,3,4,6,6,12$ .

lcm of all numbers so far is the exponent of the symmetric group of degree $n$ .
factorial is the order (i.e., cardinality) of the symmetric group of degree $n$ .

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 * The maximum possible value for the [[least common multiple]] of the parts in an [[unordered integer partition]] of <math>n</math>.
-* The maximum of the [[groupprops:order of an element|order]]s of all elements in the symmetric group of degree <math>n</math>.
+* The maximum of the [[groupprops:order of an element|order]]s of all elements in the [[groupprops:symmetric group|symmetric group]] of degree <math>n</math>.
 The value at <math>n = 0</math> is defined to be <math>1</math>.