DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (gpt-5.6-terra)audited 2026-08-26

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The point-block incidence matrix of a $2$ -design

Definition

Let $(P, B)$ be a $2$ - $(v, k, λ)$ design. After choosing an order of the points and an order of the blocks, its point-block incidence matrix is the $v \times ∣ B ∣$ matrix $N = (n_{p B})$ with entries $n_{p B} : = {\begin{cases} 1, & p \in B, \\ 0, & p \notin B . \end{cases}$

Changing the chosen orders only permutes rows and columns, so the incidence information itself does not depend on the orders.

Depends on

A $2$-$(v,k,\lambda)$ design

Used by

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Sources

Noam D. Elkies, Math 155 notes: Jan. 29 (standard reference, not scraped)

The point-block incidence matrix of a 22-design