Weight Strings

is the Free Monoid generated by the elements of $A$ , equivalently the set of strings, including the empty string, whose letters are from $A$ ). Then the $a$ -''weight'' of $c$ , denoted by $\mathrm{wt}_a(c)$ , is the number of times the generator $a$ occurs in the unique expression for $c$ as a product (concatenation) of letters in $A$ .

A

\mathrm{wt}(c)

c

,
often simply referred to as "weight", is the number of nonzero letters in

c

.

EXAMPLES

y

c

\mathrm{wt}_y(c)=5

Let $A=\mathbf{Z}_3=\{0,1,2\}$ (an abelian group) and $c=002001200$ . Then $\mathrm{wt}_0(c)=6$ , $\mathrm{wt}_1(c)=1$ , $\mathrm{wt}_2(c)=2$ and $\mathrm{wt}(c)=\mathrm{wt}_1(c)+\mathrm{wt}_2(c)=3$ .

	CATEGORIES ABOUT WEIGHT STRINGS

	semigroup theory

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