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For questions that explicitly reference the binomial coefficients, Pascal's Triangle, and Binomial identities.
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Binomial coefficient in a binomial coefficient
I am doing some research in combinatorics, and I found that I have to consider the following binomial coefficient :
$$ \binom{\binom{i}{j}}{k} $$
(In fact, I have to take the product for fixed $i,k$ a …
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Inequalities between sums of products of certain binomial coefficients
I am a PhD student. During my researches, I often have to deal with inequalities involving sums of binomial coefficients, where the sums are indexed by some set of integer compositions. For example, l …