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 Fisher's Inequality
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Source Fisher's inequality (Wikipedia)
Principal Result Of
Source Fisher's inequality (Wikipedia)
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Source Fisher's inequality (Wikipedia)
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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
Principal Result Of: Ronald Fisher, Lead sentence of the article on the result
Outlined by Ronald Fisher, a population geneticist and statistician, who was concerned with the design of experiments such as studying the differences among several different varieties of plants, under each of a number of different growing conditions, called blocks.
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
In Group: Enumerative, Additive and Algebraic Combinatorics, Lead section
of subsets that satisfy certain prescribed conditions in combinatorial mathematics. Outlined by Ronald Fisher, a population geneticist
In Branch: Combinatorics, Lead section
of subsets that satisfy certain prescribed conditions in combinatorial mathematics. Outlined by Ronald Fisher, a population
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