Weight (strings)

Summary

The $a$-weight of a string, for a letter $a$, is the number of times that letter occurs in the string. More precisely, let $A$ be a finite set (called the alphabet), $a\in A$ a letter of $A$, and $c\in A^*$ a string (where $A^*$ 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 $A$.