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.
A Latin-square assignment is a strict subset of RCBD assignments
Example
With treatments , the cyclic array is a Latin square. The array with all three rows equal to is an allowed RCBD assignment of three blocks, but is not a Latin square. Under the uniform RCBD law that particular assignment has probability ; under the uniform Latin-square law it has probability zero.
Verification
Given: Three treatments, three blocks, and the two displayed assignments in the Example.
[F1] An RCBD assignment consists of an independently randomized treatment permutation in each block (Randomized complete-block design).
[F2] A Latin-square assignment uses every treatment once in every row and every column, and the specified law is uniform on all such squares (Randomized Latin-square design).
In the cyclic array, each row and each column contains once, so it belongs to the Latin-square sample space.
In the repeated-row array, each row contains once, so it is an RCBD assignment; each column repeats a single treatment, so it is not a Latin square.
There are permutations per RCBD block and the blocks are independently uniform, so the particular repeated-row assignment has probability . It has probability zero under a law supported only on Latin squares.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
5 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
- Gary W. Oehlert, A First Course in Design and Analysis of Experiments, Chapter 13 §13.3.2 (standard reference, not scraped)