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Bluelink 1 book for verifiability (prndis)) #IABot (v2.0.1) (GreenC bot |
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There are other methods of determining a sequence's validity based on the flavor of siteswap.
A '''vanilla''' siteswap sequence <math>a_0a_1a_2...a_{n-1}</math>where <math>n</math> is the period of the siteswap, is valid when the [[cardinality]] of the set <math>S</math> (written in [[Set-builder notation]]) is equal to the period <math>n</math> where<math display="block">S=\{(a_i+i)\bmod n | 0\leq i\leq n-1\}</math>To find if a pattern is valid, first create a new sequence formed by adding <math>0</math> to the first number, <math>1</math> to the second number, <math>2</math> to the
For example, the pattern 531 would produce <math>5+0,3+1,1+2 </math> or <math>5,4,3</math>. Since the pattern 531 has a period of 3, The results from the previous example would produce <math>5\bmod 3,4\bmod 3,3\bmod 3</math>or <math>2,1,0</math>. In this case, 531 is valid since the numbers <math>2,1,0</math> are all unique. Another example, 513 is an invalid pattern because the first step produces <math>5+0,1+1,3+2 </math> or <math>5,2,5</math>, the second step produces <math>5\bmod 3,2\bmod 3,5\bmod 3</math> or <math>2,2,2</math>, and the final sequence contains at least a duplicate of one number, in this case a 2.
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