Douglas Blumeyer's RTT How-To: Difference between revisions

|+ '''Table 6a.''' Complement sign flipping sequences by rank and dimensionality

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So in this case:

An important observation to make about multicommas and multimaps is that — for a given temperament — they always have the same count of terms. This may surprise you, since the rank and nullity for a temperament are often different, and the length of the multimap comes from the rank while the length of the multicomma comes from the nullity. But there’s a simple explanation for this. In either case, the length is not directly equal to the rank or nullity, but to the dimensionality choose the rank or nullity. And there’s a pattern to combinations that can be visualized in the symmetry of rows of Pascal’s triangle: <span><math>{d \choose n}</math></span> is always equal to <span><math>{d \choose {d - n}}</math></span>, or in other words, <span><math>{d \choose n}</math></span> is always equal to <span><math>{d \choose r}</math></span>. Here are some examples:

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|+'''Table 6b.''' Multi(co)vector prime combinations (<math>r</math> can be switched for <math>n</math>)

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Each set of one side corresponds to a set in the other side which has the exact opposite elements.