moderately difficult
[?] The result of the problem is known, but I am uncertain whether a combinatorial proof is known.
[∗] A combinatorial proof of the problem is not known. In all cases, the result of the problem is known.
PROBLEM: The number of subsets of an
PROOF: A way of choosing element can be described as a binary number, and the number of ways is
PROBLEM: A composition of
PROOF: Using “Stars and bars” method, there will be some bars to divide
PROBLEM: The total number of parts of all compositions of
PROOF: I consider that using power series is extremely easy, but we can’t use it…
Still using “Stars and bars” method, we consider that a bar in