Parameters measuring the size of set families - Combinatorial Parameters

Oriented Diameter

Name: Oriented Diameter

Symbol: $\mathrm{D}^+$

Definition:

The oriented diameter $\mathrm{D}^+(\mathcal{H})$ of a family $\mathcal{H}$ is defined as $$ \mathrm{D}^+(\mathcal{H}):= \max{|S|: {\emptyset, S}\subset \mathcal{H}_{|S}} $$

Category: Basic

Symmetric: No

Monotonic: Yes

P-Monotonic: Yes

Doubly Monotonic: Yes

Strictly Monotonic: No