# Residue

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**Residue** is a concept in incidence systems that generalizes the concept of sections on abstract polytopes.

## Definition[edit | edit source]

The **residue** of a flag, F, in an incidence geometry, , is an incidence system where

- is the set of elements of Γ, not in F, that are incident on every element of F.
- is the set of types of , . It is equivalent to .
- is * restricted to the domain of .
- is t restricted to the domain of .

An incidence structure is **residually connected** if every residue of rank 2 or greater has a connected incidence graph.

## Bibliography[edit | edit source]

- Fernandes, Maria (2014). "Regular and chiral hypertopes" (PDF).

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