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''). | ||
* Circular words may be treated as (based) infinite words. Thus for ''m'', ''n'' integers, ''m'' < ''n'', then ''s''[''m''] denotes ''s''[''m'' mod {{len|''s''}}]. The notation ''s''[''m'':''n''] denotes the (''n'' − ''m'')-letter word ''s''[''m'']''s''[''m''+1]...''s''[''n''−1], where all indices are taken mod {{len|''s''}}. | * Circular words may be treated as (based) infinite words. Thus for ''m'', ''n'' integers, ''m'' < ''n'', then ''s''[''m''] denotes ''s''[''m'' mod {{len|''s''}}]. The notation ''s''[''m'':''n''] denotes the (''n'' − ''m'')-letter word ''s''[''m'']''s''[''m''+1]...''s''[''n''−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'']. | * 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). | ||
== Algebraic structures == | == Algebraic structures == | ||