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A parting of n is a list P=(a1,a2,a3,....) such that a1<=a2<=a3.... and n=a1+a2+a3+... For example for n=5 the partings are: (1,1,1,1,1), (1,1,1,2),(1,1,3),(1,2,2),(1,4),(2,3),(5) Define X(P) as the number of 1s in a parting and Y(P) as the number of different numbers, for example X(1,1,1,2)=3 and Y(1,1,1,2)=2. For a certain n, show that the sum of all X(P) is equal to the sum of all Y(P), for example for n=5 both are equal to 12
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Data Scientist

Interviewed at Pagaya

3.3★
Dec 22, 2020

A parting of n is a list P=(a1,a2,a3,....) such that a1<=a2<=a3.... and n=a1+a2+a3+... For example for n=5 the partings are: (1,1,1,1,1), (1,1,1,2),(1,1,3),(1,2,2),(1,4),(2,3),(5) Define X(P) as the number of 1s in a parting and Y(P) as the number of different numbers, for example X(1,1,1,2)=3 and Y(1,1,1,2)=2. For a certain n, show that the sum of all X(P) is equal to the sum of all Y(P), for example for n=5 both are equal to 12

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