# Flag in an incidence system

From Groupprops

This term is related to: incidence geometry

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## Contents

## Definition

### Symbol-free definition

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

### Definition with symbols

Let be an incidence system. Then, a flag in is a set of pairwise incident elements of , viz a set such that for any .

### 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}}