Fisher's Inequality states that in any balanced incomplete block design, a combinatorial arrangement of points into blocks in which every pair of points appears together in the same fixed number of blocks, the number of blocks can never be smaller than the number of points. Named for Ronald Fisher, it is a foundational result of combinatorial design theory.
Facts
StatementIn a balanced incomplete block design with v points and b blocks, b is at least v. 2 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Proved By
Source Fisher's inequality (Wikipedia)
Sources
1. Wikipedia: Fisher's inequality
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
Fisher's inequality is a necessary condition for the existence of a balanced incomplete block design, that is, a system of subsets that satisfy certain prescribed conditions in combinatorial mathematics.
2. Fisher's inequality (Wikipedia)
Introduction
Fisher's inequality states simply that b ≥ v.
References
R. A. Fisher, 'An examination of the different possible solutions of a problem in incomplete blocks', Annals of Eugenics, volume 10, 1940
Proved By: Ronald Fisher, Lead paragraph
Fisher's inequality is a necessary condition for the existence of a balanced incomplete block design, that is, a system of subsets
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