,the largest known prime number that counts a number of partitions is " p " ( 120052058 ), with 12198 decimal digits.
12.
The idly steam plate has number of partitions in which the batter is poured-" ittu "; and after it is steam cooked " avi ".
13.
Both DOS and DOS-VS allow the number of partitions to be set at IPL ( Initial Program Load ), the IBM term for Boot load.
14.
Sometimes Dobinski's formula is stated as the number of partitions of a set of size " n " equals the " n " th moment of that distribution.
15.
That is, we take the limit as the largest of the partitions approaches zero in size, so that all other partitions are smaller and the number of partitions approaches infinity.
16.
Therefore, according to the representation theory of a finite group, the number of inequivalent irreducible representations, over the complex numbers, is equal to the number of partitions of " n ".
17.
Therefore according to the representation theory of a finite group, the number of inequivalent irreducible representations, over the complex numbers, is equal to the number of partitions of " n ".
18.
The " coefficient " in each term is the number of partitions of a set of members that collapse to that partition of the integer when the members of the set become indistinguishable.
19.
Since, by conjugation of partitions, this is the same as the number of partitions of " m " into parts of size at most " n ", by identification of generating series we obtain the identity:
20.
When d = 2 this becomes the special case, known as Euler's theorem, that the number of partitions of N into distinct parts is the same as the number of partitions of N into odd parts.
