The maximum likelihood probability of unique-singleton, ternary, and length-7 patterns

We derive several pattern maximum likelihood (PML) results, among them showing that if a pattern has only one symbol appearing once, its PML support size is at most twice the number of distinct symbols, and that if the pattern is ternary with at most one symbol appearing once, its PML support size is three. We apply these results to extend the set of patterns whose PML distribution is known to all ternary patterns, and to all but one pattern of length up to seven.