Parameters measuring the size of set families - Combinatorial Parameters

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Log Size Ratio

Name: Log Size Ratio

Symbol: $\frac{\log (\mathrm{H}-1)}{\log (n+1)}$

Definition:

The Log Size Ratio of a family $\mathcal{H}$ is the ratio of the log of its cardinality to the log of the effective range, $$ \log \frac{|\mathcal{H|}-1}{\log (n+1)} $$

Category: Basic

Symmetric: Yes

Monotonic: Yes

P-Monotonic: Yes

Doubly Monotonic: Yes

Strictly Monotonic: No

Values:

Relationships (as Parameter 1): None

Relationships (as Parameter 2):