(7,3,1)-design
C29197
concept
A (7,3,1)-design is a combinatorial incidence structure consisting of 7 points and 7 three-point blocks such that every pair of distinct points lies together in exactly one block.
All labels observed (2)
| Label | Occurrences |
|---|---|
| (7,3,1)-design canonical | 1 |
| finite incidence structure | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: (7,3,1)-design
Generated description
A (7,3,1)-design is a combinatorial incidence structure consisting of 7 points and 7 three-point blocks such that every pair of distinct points lies together in exactly one block.
Instances (2)
| Instance | Via concept surface |
|---|---|
| Fano plane | — |
| Szekeres configuration | finite incidence structure |