Baranyai's Theorem states that whenever k divides n, the collection of all k-element subsets of an n-element set can be partitioned into perfect matchings, meaning it can be split into groups each of which itself partitions the full n-element set into disjoint k-element blocks. Named for Zsolt Baranyai, it is a foundational existence result of design theory and hypergraph combinatorics, resolving the natural generalization of round-robin tournament scheduling from ordinary graphs to uniform hypergraphs.
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StatementWhenever k divides n, the k-element subsets of an n-element set can be partitioned into perfect matchings, each one itself a partition of the full n-element set into disjoint k-element blocks. 1 Classification
Statement Form Baranyai's Theorem
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Source Baranyai's theorem (Wikipedia)
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The general case was proved by Zsolt Baranyai in 1975.
Principal Result Of: Zsolt Baranyai, Lead sentence of the article on the result
In combinatorial mathematics, Baranyai's theorem (proved by and named after Zsolt Baranyai) deals with the decompositions of complete hypergraphs.
Proved By: Zsolt Baranyai, Lead
The general case was proved by Zsolt Baranyai in 1975.
In Branch: Combinatorics, Lead paragraph
In combinatorial mathematics, Baranyai's theorem (proved by and named after Zsolt Baranyai) deals with the decompositions of complete hypergraphs.
In Group: Enumerative, Additive and Algebraic Combinatorics, Lead section
In combinatorial mathematics, Baranyai's theorem (proved by and named after
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