User:Inthar/Style guide: Difference between revisions
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* The length of a linear, based circular, or free circular word ''s'' is denoted {{len|''s''}} or len(''s''). | * The length of a linear, based circular, or free circular word ''s'' is denoted {{len|''s''}} or len(''s''). | ||
* For circular words ''s'', if ''i'' < ''j'' the slice notation ''s''[''i'':''j''] denotes the (''j'' − ''i'')-letter word ''s''[''i'']''s''[''i''+1]...''s''[''j''−1], where all indices are taken mod {{len|''s''}}. | * For circular words ''s'', if ''i'' < ''j'' the slice notation ''s''[''i'':''j''] denotes the (''j'' − ''i'')-letter word ''s''[''i'']''s''[''i''+1]...''s''[''j''−1], where all indices are taken mod {{len|''s''}}. | ||
* Shifts: If ''s'' is a circular or infinite word, then for <math>k \in \mathbb{Z}, \ \sigma^k(s) = (x \mapsto s[x+k])</math> denotes ''s'' shifted to the left by ''k'' letters. | |||
* Substitution: If ''w'' is a linear or based circular word in '''X''' and possibly other letters, and ''u'' is a based circular word, then <math>\mathsf{subst}(w, \mathbf{X}, u)</math> denotes the word ''w'' but with the ''i''th occurrence of '''X''' replaced with ''u''[''i''] (for ''i'' ≥ 0). | * Substitution: If ''w'' is a linear or based circular word in '''X''' and possibly other letters, and ''u'' is a based circular word, then <math>\mathsf{subst}(w, \mathbf{X}, u)</math> denotes the word ''w'' but with the ''i''th occurrence of '''X''' replaced with ''u''[''i''] (for ''i'' ≥ 0). | ||