and the antitriplet must be in an octet state (as is the case for red–antigreen), and not a singlet. The multiplicity, $N$, of the multiplet $\{p,q\}$ is then given by: $$N = \frac{1}{2} (p+1)(q+1)(p+q+2).
\label{eq:multiplicityrev}$$

The result of adding a set of triplets and antitriplets can be calculated in an iterative way. Starting from a multiplet $\{p,q\}$ adding one more triplet, with random colour, one obtains the multiplets $$\{p+1,q\},\,\,\, \{p-1,q+1\},\,\, \mathrm{and}\,\, \{p,q-1\}, 
\label{eq:randomaddition}$$ with weights proportional to the corresponding multiplicities given by [eq. (\[eq:multiplicityrev\])]{}. From symmetry, the addition of an antitriplet gives the multiplets $\{p,q+1\}$, $\{p+1,q-1\}$, and $\{p-1,q\}$. Multiplets with negative values for $p$ or $q$ are not allowed. In [appendix [\[sec:pq-calc\]]{}]{} the result for adding random colour octets (corresponding to gluons) is also described.

The average walk can be easily calculated numerically, and in [figure [\[fig:ranwalk\]]{}]{} we show $\langle p+q\rangle$ obtained from randomly adding triplets and antitriplets, with a fixed number, $m+n$, of charges. (The individual numbers $m$ and $n$ are then given by a binomial distribution. The same result was also presented in ref. [@Biro:1984].) The width of the distribution is indicated by the band showing $1\,\sigma$ variations.

Rope tension {#sec:ropetension}
------------

As mentioned in the introduction, lattice 