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Proving ${l\choose n}+nl-{d+n\choose d}<0$ for $n\geq 6$, $d\geq 3$, $l<d+n-1$

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#inequality #binomial-coefficients
61
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Series evaluation

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#summation #binomial-coefficients #binomial-distribution
395
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Graphing the binomial coefficients: appearances?

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#binomial-coefficients
35
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solving polynomial equation (showing non-negativity)

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#induction #binomial-coefficients #systems-of-equations #alternative-proof
96
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Approximation of binomial coefficients

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#summation #binomial-coefficients #approximation
68
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Laurent Series Expansion and Convergence Proof

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#sequences-and-series #complex-analysis #complex-numbers #binomial-coefficients #laurent-series
645
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Distributing identical balls in boxes with minimum and maximum per box

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#combinatorics #binomial-coefficients #generating-functions
133
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Prove that ${n \choose k} \ge (\frac{n}{k})^k$ for any given $n \ge k$ using induction

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#combinatorics #induction #binomial-coefficients
117
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Coefficients of a polynomial

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#polynomials #summation #binomial-coefficients
477
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Sum of Product of Central Binomial Coefficients

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#combinatorics #binomial-coefficients #multinomial-coefficients
55
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binomial coefficient aproximation

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#binomial-coefficients
56
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Coins to be put in empty purses

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#combinatorics #binomial-coefficients
122
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An Identity for a Fibbonacci-Type Polynomial

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#polynomials #summation #recurrence-relations #binomial-coefficients #function-and-relation-composition
140
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How many adjacent triplets do triplets have on average in an Erdos-Renyi graph?

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#combinatorics #graph-theory #binomial-coefficients #random-graphs
75
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Proving an identity of partial binomial sum from a statistical context without using combinatorics

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#binomial-coefficients #order-statistics

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