User:Inthar/Style guide: Difference between revisions
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* A ''(free) circular word'' is a class of based circular words equivalent under rotation: <math>\{x\mapsto s[x], x\mapsto s[x+1], ..., x\mapsto s[x+|s|-1] \}</math> for ''s'' a based circular word. | * A ''(free) circular word'' is a class of based circular words equivalent under rotation: <math>\{x\mapsto s[x], x\mapsto s[x+1], ..., x\mapsto s[x+|s|-1] \}</math> for ''s'' a based circular word. | ||
* 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''). | ||
* Circular words may be treated as (based) infinite words. For circular words, 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''}}. | * Circular words may be treated as (based) infinite words. 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''}}. | ||
* Substitution: If ''w'' is a linear or based circular word in '''X''' and possibly other letters, and ''u'' is a based circular word in '''b''' and '''c''', 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 in '''b''' and '''c''', 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). | ||