Addition chains are decomposed into determiners and regulators to obtain identities for aggregate sums and harmonic profiles, enabling chain comparison and a balancing optimization problem.
71, Siam, 2000
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
years
2020 4verdicts
UNVERDICTED 4representative citing papers
Improved bounds Δ(s) ≪ s^{-(3/2-ε)} (upper) and Δ(s) ≫ (log s) s^{-3/2} (lower) for the minimal triangle area with s points in the unit disk.
Lower bounds on coincidence points for multiplicative and additive functions are obtained, varying with period length and worst-case growth rates of consecutive value ratios.
Using the compression method, the paper derives lower bounds C sqrt(k)/2 n^{1+o(1)} for unit distances and D sqrt(k)/2 n^{2/k - o(1)} for distinct distances in R^k.
citing papers explorer
-
On the distribution of addition chains
Addition chains are decomposed into determiners and regulators to obtain identities for aggregate sums and harmonic profiles, enabling chain comparison and a balancing optimization problem.
-
New bounds for the Heilbronn triangle problem
Improved bounds Δ(s) ≪ s^{-(3/2-ε)} (upper) and Δ(s) ≫ (log s) s^{-3/2} (lower) for the minimal triangle area with s points in the unit disk.
-
On the pointwise periodicity of multiplicative and additive functions
Lower bounds on coincidence points for multiplicative and additive functions are obtained, varying with period length and worst-case growth rates of consecutive value ratios.
-
On the Erd\H{o}s distance problem
Using the compression method, the paper derives lower bounds C sqrt(k)/2 n^{1+o(1)} for unit distances and D sqrt(k)/2 n^{2/k - o(1)} for distinct distances in R^k.