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.
Facts
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 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.
Sources
1. Baranyai's theorem (Wikipedia)
Wikimedia FoundationHistory sectionQuote, History section
The general case was proved by Zsolt Baranyai in 1975.
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