Saturday, 30 July 2016

combinatorics - Combinatorial proof of sumlimitsmi=02ninchooseimchoosei=sumlimitsmi=0n+michoosemnchoosei

I've been wondering for a while how to solve (prove) a combinatorial identity, using just combinatorial interpretation:



mi=02ni(ni)(mi)=ni=0(n+mim)(ni)



(mn )



The left hand side is pretty much about choosing any number of elements from the set M={a1,,am} and then choosing at least the same amount from N={b1,,bn}, but I can't see how the right hand side satisfies that.

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