Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Sunflowers, petals, and their common core
Definition
Let with . Distinct finite sets form an -petal sunflower if there is a set such that
The set is the core, the sets are the flowers, and the pairwise disjoint sets are the petals. Equivalently, form a sunflower precisely when their pairwise intersections are all equal.
A sunflower is -uniform when every flower has cardinality . The core may be empty; in that case the flowers themselves are pairwise disjoint.
Depends on
Used by
- Four explicit petals with a common two-element core form a sunflower Example
- A maximal pairwise disjoint subfamily either supplies a sunflower or gives a small transversal for the whole uniform family Lemma
- Erdős-Rado sunflower lemma: more than k!(r-1)ᵏ distinct k-sets contain an r-petal sunflower Theorem
Dependency tree · two levels
8 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Sunflower (mathematics) (Wikipedia) (standard reference, not scraped)