The collation or lexicographical ordering of a dictionary generally depends upon its writing system. The most frequently used orders are numerical order and lexicographical order. This was mentioned on the BBC lexicographical programme "Balderdash and Piffle". The third system of lexicographical ordering is by character pronunciation. There are several variants and generalizations of the lexicographical ordering. These multi-sets can be well-ordered by lexicographical ordering (monotonically decreasing). This generalized lexicographical order is a total order if each factor set is totally ordered. This influenced later volumes of this and other lexicographical works. Tones are noted solely in lexicographical works. This is because radicals are merely arbitrarily chosen categories for lexicographical purposes. In his lexicographical work he collaborated with William Lloyd. The bopomofo style keyboards are in lexicographical order, top-to-bottom left-to-right. This variant of the lexicographical order is sometimes called "shortlex order". Use column and box swaps to achieve the lowest lexicographical ID. One of these admissible orders is the lexicographical order.