Is the expression on the right-hand side of the equation correct? Here’s why I’m asking: For , the denominator of this expression is , or , so the fraction reduces to . But this implies that for all , which is not true.

David

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Is the expression on the right-hand side of the equation correct? Here’s why I’m asking: For , the denominator of this expression is , or , so the fraction reduces to . But this implies that for all , which is not true.

David

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Maybe it is supposed to say that every part is strictly less than , not less than or equal to. Because then that would be true since it’s just the one composition of all 1’s, right?

Hannah

Hannah is right; should be the number of compositions of such that all parts are *strictly less* than . Hannah showed us how to check the case , and I encourage you to also think about the case .

Thanks for the heads up, David.

EC1 problem 26 uses (k+1) so that would be the correct exponent in the formula. Love your lectures after buying the book (spent 2 days on hw1 problem 3 and found alternative solution based on induction) Very stimulating problems.

Frits, Amsterdam