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| The <math>a</math>-'''weight''' of a string, for <math>a</math> a letter, is the number of times that letter occurs in the string. More precisely, let <math>A</math> be a finite set (called the ''alphabet''), <math>a\in A</math> a ''letter'' of <math>A</math>, and <math>c\in A^*</math> a | | The name of the author is Nestor. Delaware is the location I love most but I need to move for my family. The preferred hobby for him and his children is to generate and now he is attempting to make money with it. Interviewing is what she does.<br><br>My site: extended car warranty ([http://Www.Dienoobs-Css.de/index.php?mod=users&action=view&id=17012 click through the next internet site]) |
| ''string'' (where <math>A^*</math> is the [[free monoid]] generated by the elements of <math>A</math>, equivalently the set of strings, including the empty string, whose letters are from <math>A</math>). Then the <math>a</math>-''weight'' of <math>c</math>, denoted by <math>\mathrm{wt}_a(c)</math>, is the number of times the generator <math>a</math> occurs in the unique expression for <math>c</math> as a product (concatenation) of letters in <math>A</math>.
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| If <math>A</math> is an [[abelian group]], the [[Hamming weight]] <math>\mathrm{wt}(c)</math> of <math>c</math>,
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| often simply referred to as "weight", is the number of nonzero letters in <math>c</math>.
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| == Examples ==
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| * Let <math>A=\{x,y,z\}</math>. In the string <math>c=yxxzyyzxyzzyx</math>, <math>y</math> occurs 5 times, so the <math>y</math>-weight of <math>c</math> is <math>\mathrm{wt}_y(c)=5</math>.
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| * Let <math>A=\mathbf{Z}_3=\{0,1,2\}</math> (an abelian group) and <math>c=002001200</math>. Then <math>\mathrm{wt}_0(c)=6</math>, <math>\mathrm{wt}_1(c)=1</math>, <math>\mathrm{wt}_2(c)=2</math> and <math>\mathrm{wt}(c)=\mathrm{wt}_1(c)+\mathrm{wt}_2(c)=3</math>.
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| {{PlanetMath attribution|id=6985|title=Weight (strings)}}
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| [[Category:Semigroup theory]]
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Latest revision as of 07:30, 11 January 2015
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