Bracketope (EntityClass, 3)

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Revision as of 08:57, 15 March 2008 by Keiji (Talk | contribs)

A bracketope is any shape which can be defined using bracket notation.

Sets of bracketopes by complexity

Totally useless bracketopes (&, ampersand)
A totally useless bracketope is a bracketope which is similar to a pure bracketope.
Partially useless bracketopes (*, asterisk)
A partially useless bracketope is a bracketope whose vertex graph is identical to that of a pure bracketope.
Pure bracketopes
A pure bracketope is a bracketope which is not partially or totally useless.
  • A question mark indicates that it is unknown whether this bracketope is pure.

Determining bracketopes' purity

If two or more bracketopes are similar to each other, the one with the lowest bracketopic index is pure and all others are totally useless.

Bracketopic statistics

Here is a table to show the number and percentage of various types of bracketopes in each dimension.

Dimension Bracketopes Totally useless Partially useless Pure Rotopes Strange rotopes Pure rotopes
1 1 0 (0%) 0 (0%) 1 (100%) 1 (100%) 0 (0%) 1 (100%)
2 3 1 (33%) 0 (0%) 2 (67%) 2 (67%) 0 (0%) 2 (67%)
3 9 0 (0%) 3 (33%) 6 (67%) 3 (33%) 0 (0%) 3 (33%)
4 36 3 (8%) 9 (25%) 24 (67%) 5 (14%) 1 (3%) 4 (11%)
5 144 0 (0%) 65 (45%) 79 (55%) 7 (5%) 2 (1%) 5 (3%)
Trend Increasing Unknown Unknown Decreasing % Decreasing % Unknown Decreasing %

Finding bracketopes

There is currently one main method for finding bracketopes:

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