Friday, 28 November 2014

combinatorics - Combinatorial identity: summation of stars and bars

I noticed that the following identity for a summation of stars and bars held for specific k but I was wondering if someone could provide a general proof via combinatorics or algebraic manipulation. I wouldn't be surprised if this is a known result; it looks very similar to the Hockey Stick identity.



ki=0(d+i1d1)=(d+kk)



The left can be immediately rewritten as ki=0(d+i1i) if it helps inspire intuition.

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