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Euler's Partition Theorem with Upper Bounds on Multiplicities
partition Euler's partition theorem Sylvester's bijection
2014/6/3
We show that the number of partitions of n with alternating sum k such that the multiplicity of each part is bounded by 2m + 1 equals the number of partitions of n with k odd parts such that the multi...
Explicit Upper Bounds for the Average Order of $d_n$ and Applications to Class Number
Multiplicative number theory Average order Class number
2008/7/3
In this paper, we prove some explicit upper bounds for the average order of the generalized divisor function, and, according to an idea of Lenstra, we use them to obtain bounds for the class number of...
A Note on the Upper Bounds for the Dispersion.
Good Lower and Upper Bounds on Binomial Coefficients
Binomial Coefficients Stirling's Formula Inequalities
2008/7/1
We provide good bounds on binomial coefficients, generalizing known ones, using some results of H. Robbins and of Sasvári.
Some p.d.f.-free Upper Bounds for the Dispersion $\sigma(X)$ and the Quantity $\sigma^{2}(X)+(x-EX) ^{2}$
Quantity Dispersion p.d.f.-free Upper Bounds
2008/6/26
Some p.d.f.-free Upper Bounds for the Dispersion $\sigma(X)$ and the Quantity $\sigma^{2}(X)+(x-EX) ^{2}$.
On upper bounds for infinite Prandtl number convection with or without rotation
On upper bounds infinite Prandtl number convection without rotation
2014/4/4
Bounds for the bulk heat transport in Rayleigh-Benard convection for an in nite Prandtl number uid are derived from the primitive equations. The enhancement of heat transport beyond the minimal conduc...