# Flag in an incidence system

This term is related to: incidence geometry
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## Definition

### Symbol-free definition

A flag in an incidence system is a set of pairwise incident elements.

### Definition with symbols

Let $(G,*,t,I)$ be an incidence system. Then, a flag in $G$ is a set $\Phi$ of pairwise incident elements of $G$, viz a set $\Phi$ such that $x * y$ for any $x,y \in \Phi$.

### Graph-theoretic definition

A flag in an incidence system is what corresponds to a clique in the corresponding partite graph.

## Terminology

### Rank and type of a flag

The type of a flag is the set of types of all its elements. The rank of a flag is the cardinality of the flag (and also of the type, since all elements of the flag are drawn from different types).

### Corank and cotype of the flag

The cotype of a flag is the complement (in the set of all types) of the type of the flag. The corank is the cardinality of the cotype.

### Residual incidence system

{{furtherresidual incidence system}}