Talk:Coolout Conjecture: Difference between revisions
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Created page with "The phrase "internally consistent with being part of a still life" is rather vague. I think it should be rephrased to make it clearer which patterns are or are not eligible. ~~~~" |
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The phrase "internally consistent with being part of a still life" is rather vague. I think it should be rephrased to make it clearer which patterns are or are not eligible. [[User:77topaz|77topaz]] ([[User talk:77topaz|talk]]) 03:58, 31 January 2018 (UTC) | The phrase "internally consistent with being part of a still life" is rather vague. I think it should be rephrased to make it clearer which patterns are or are not eligible. [[User:77topaz|77topaz]] ([[User talk:77topaz|talk]]) 03:58, 31 January 2018 (UTC) | ||
:There may not be sufficient documentation of the conjecture to determine this precisely. However, I believe the natural reading would be "every 3×3 area of the partial (or smaller, if overlapping with the partial's edges) is capable of occurring in a still life". | |||
:Schroeppel's original counterexample, and its 5×2 version, suffice to disprove actually even a stronger condition of 4×4-consistency (their 4×2 left ends could be extended into a [[shillelagh]] and [[hook with tail]] respectively) or also e.g. range 2 [[von Neumann neighborhood]] consistency. --[[User:Tropylium|Tropylium]] ([[User talk:Tropylium|talk]]) 11:35, 15 July 2026 (UTC) | |||
Revision as of 11:35, 15 July 2026
The phrase "internally consistent with being part of a still life" is rather vague. I think it should be rephrased to make it clearer which patterns are or are not eligible. 77topaz (talk) 03:58, 31 January 2018 (UTC)
- There may not be sufficient documentation of the conjecture to determine this precisely. However, I believe the natural reading would be "every 3×3 area of the partial (or smaller, if overlapping with the partial's edges) is capable of occurring in a still life".
- Schroeppel's original counterexample, and its 5×2 version, suffice to disprove actually even a stronger condition of 4×4-consistency (their 4×2 left ends could be extended into a shillelagh and hook with tail respectively) or also e.g. range 2 von Neumann neighborhood consistency. --Tropylium (talk) 11:35, 15 July 2026 (UTC)