google-deepmind / google-deepmind/alphaevolve_repository_of_problems
Question about third autocorr inequality
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Description
Hi, thanks for your great work! I have a question about the evaluation for the third autocorr inequality. In the codebook, it shows that
```
C_upper_bound = abs(2 * len(height_sequence_3) * np.max(convolution_3) / (np.sum(height_sequence_3)**2))
```
But follow the definition
$\max_{-1/2 \leq t \leq 1/2} \left|f*f(t)\right| \geq C_3 \left(\int_{-1/4}^{1/4} f(x)\ dx\right)^2$
, should it be
```
C_upper_bound = 2 * len(height_sequence_3) * np.max(abs(convolution_3)) / (np.sum(height_sequence_3)**2)
```
If using this formula, seems both previous 1.4581 and current 1.4557 bound can not be obtained. So wonder if there is any problem or I mis-understand something. Thanks!
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