Question

What is integer partition? Write down all partitions of 8. Also find and .

Answer 1

in number theory and combinatorics,a partition of a positive integer n,also called an integer partition,is a way of writing n as a sum of positive integers.two sums that differ only in the order of their summands are considered the same partition.

Answer 2

An integer partition of a positive integer n is a way of writing n as a sum of positive integers. There are 22 partitions of the number 8.

• To find the integer partitions of 8, we divide the integer 8 into various combinations of positive integers in the following way-

7+1

6+2

6+1+1

5+3

5+2+1

5+1+1+1

4+4

4+3+1

4+2+1+1

4+1+1+1+1

3+5

3+4+1

3+3+2

3+2+1+1+1

3+1+1+1+1+1

2+6

2+5+1

2+4+1+1

2+3+1+1+1

2+2+1+1+1+1

2+1+1+1+1+1+1

1+1+1+1+1+1+1+1

• Hence, in total, there are 22 partitions of the number 8.

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