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Fungrim entry: d1438d

BnBm≤Bn+m≤(n+mn)BnBmB_{n} B_{m} \le B_{n + m} \le {n + m \choose n} B_{n} B_{m}
Assumptions:n∈Z≥0  and⁡  m∈Z≥0n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; m \in \mathbb{Z}_{\ge 0}
References:
  • https://arxiv.org/abs/math/0104137
TeX:
B_{n} B_{m} \le B_{n + m} \le {n + m \choose n} B_{n} B_{m}

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; m \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
BellNumberBnB_{n} Bell number
Binomial(nk){n \choose k} Binomial coefficient
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("d1438d"),
    Formula(LessEqual(Mul(BellNumber(n), BellNumber(m)), BellNumber(Add(n, m)), Mul(Mul(Binomial(Add(n, m), n), BellNumber(n)), BellNumber(m)))),
    Variables(n, m),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(m, ZZGreaterEqual(0)))),
    References("https://arxiv.org/abs/math/0104137"))

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2021-03-15 19:12:00.328586 UTC