- #1
quantumfireball
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In How many ways can one write a natural number M as a sum of N whole numbers?
Consider the two conditions;
1)the numbers appearing in the sum are distinct.
2)the numbers appearing in the sum are not necessary distinct.
eg1:eight can be written as a sum of 6 whole numbers as shown below
8=8+0+0+0+0+0
8=1+1+1+1+4+0
etc..(subject to condition 2)
eg2:8 can be written as a sum of 4 whole numbers as shown below
8=0+1+3+4
etc..(subject to condition 1)
Let me make the following notations
[tex]\Gamma[/tex](M,N) as the no of ways to partition M into N whole numbers subject to condition 1)
[tex]\Pi[/tex](M,N) as the no of ways to partition M into N whole numbers subject to condition 2)
this is no homework problem i formulated this on my own.
Consider the two conditions;
1)the numbers appearing in the sum are distinct.
2)the numbers appearing in the sum are not necessary distinct.
eg1:eight can be written as a sum of 6 whole numbers as shown below
8=8+0+0+0+0+0
8=1+1+1+1+4+0
etc..(subject to condition 2)
eg2:8 can be written as a sum of 4 whole numbers as shown below
8=0+1+3+4
etc..(subject to condition 1)
Let me make the following notations
[tex]\Gamma[/tex](M,N) as the no of ways to partition M into N whole numbers subject to condition 1)
[tex]\Pi[/tex](M,N) as the no of ways to partition M into N whole numbers subject to condition 2)
this is no homework problem i formulated this on my own.