Parameters measuring the size of set families - Combinatorial Parameters

Diameter

Name: Diameter

Symbol: $\mathrm{D}$

Definition:

The diameter $D(\mathcal{H})$ of a family $\mathcal{H}$ is the largest distance between two elements of the family, i.e. $$ D(\mathcal{H}):= \max_{h_1,h_2\in\mathcal{H}} |h_1\Delta h_2| $$

Comments:

The diameter is equal to the strict diameter dimension.

Category: Basic

Symmetric: Yes

Monotonic: Yes

P-Monotonic: Yes

Doubly Monotonic: Yes

Strictly Monotonic: No