Incidence structure

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This term is related to: incidence geometry
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WARNING: POTENTIAL TERMINOLOGICAL CONFUSION: Please don't confuse this with incidence system

Definition

An incidence structure is an incidence system with two types: points and blocks.

Equivalently, it can be viewed as a bipartite graph with the two parts separated, marked, and labelled as the points versus the blocks.

Notions

Dual incidence structures

The dual of an incidence structure is the incidence structure obtained by interchanging the role of points and blocks. In graph-theoretic terms, it is obtained by relabelling the vertex set of points as blocks, and the vertex set of blocks as points.

Complementary incidence structure

The complementary incidence structure to a given incidence structure is the incidence structure obtained by taking the complement of the graph associated with the incidence structure.

Parameters

Let v be the number of points and b the number of blocks. We define v_m as the average number of points on m blocks and b_m denotes the average number of blocks incident on m points.