Counting using products.

Today I proved the binomial theorem for my class. I did an informal proof showing them how, if we consider the set containing the alphabet: and the following product. expanding this produces a sum with every combination of the letter a-z: if we count all of the terms in this sum with, say three elements, […]

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Counting integer partitions

My close friend Owen introduced me to generating functions last year. I was not impressed at first since they seemed cumbersome... but now I see how powerful they are for counting partitions. So, I will share my understanding of this matter. This post is based on my readings of The Theory of Partitions, by George […]

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