Generator-offset property: Difference between revisions

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* An ''odd-step'' is a ''k''-step where ''k'' is odd; an ''even-step'' is defined similarly.

* Given a linear or cyclic word ''S'' with a step size X, define ''E''<sub>X</sub>(''S'') as the scale word resulting from deleting all instances of X from ''S''.

* By a ''subword'', ''substring'', or ''slice'' on index ''i'' of a word ''S'', denoted ''S''[''i'' : ''j''], ~~we mean~~

* By a ''subword'', ''substring'', or ''slice'' on index ''i'' of a word ''S'', denoted ''S''[''i'' : ''j''],

** ''S''[''i''] ''S''[''i'' + 1] ... ''S''[''j'' − 1] ''S''[''j''] if ''j'' > ''i'',

** ''S''[''i''] ''S''[''i'' + 1] ... ''S''[len(''S'')] S[1] ...''S''[''j'' − 1] ''S''[''j''] if ''j'' < ''i'',

** ''S''[''i''] when ''j'' = ''i''.

* The indices above are 1-indexed. If indices are out of bounds we first replace ''i'' and ''j'' with ''i'' % len(''S'') + 1 and ''j'' % len(''S'') + 1.

* Given a mos aX bY, a ''chunk'' of X's is a maximal substring made of X's, bounded by Y's, possibly empty. We do not include the boundary Y's.

* An ''n''-''ary'' scale is a scale with ''n'' different step sizes. ''Binary'' and ''ternary'' are used when ''n'' = 2 and 3 respectively.

@@ Line 28: / Line 28: @@
 * An ''odd-step'' is a ''k''-step where ''k'' is odd; an ''even-step'' is defined similarly.
 * Given a linear or cyclic word ''S'' with a step size X, define ''E''<sub>X</sub>(''S'') as the scale word resulting from deleting all instances of X from ''S''.
-* By a ''subword'', ''substring'', or ''slice'' on index ''i'' of a word ''S'', denoted ''S''[''i'' : ''j''], we mean
+* By a ''subword'', ''substring'', or ''slice'' on index ''i'' of a word ''S'', denoted ''S''[''i'' : ''j''],
 ** ''S''[''i''] ''S''[''i'' + 1] ... ''S''[''j''  &minus; 1] ''S''[''j''] if ''j'' > ''i'',
 ** ''S''[''i''] ''S''[''i'' + 1] ... ''S''[len(''S'')] S[1] ...''S''[''j''  &minus; 1] ''S''[''j''] if ''j'' < ''i'',
 ** ''S''[''i''] when ''j'' = ''i''.
+* The indices above are 1-indexed. If indices are out of bounds we first replace ''i'' and ''j'' with ''i'' % len(''S'') + 1 and ''j'' % len(''S'') + 1.
 * Given a mos aX bY, a ''chunk'' of X's is a maximal substring made of X's, bounded by Y's, possibly empty. We do not include the boundary Y's.
 * An ''n''-''ary'' scale is a scale with ''n'' different step sizes. ''Binary'' and ''ternary'' are used when ''n'' = 2 and 3 respectively.