Maximal Color Patterns

The last section described how to determine if a color pattern is weaveable and, if so, how to create a draft for it. This section looks at weaveable color patterns from a different perspective: How to create color patterns that are guaranteed to be weaveable and have as many colors as are possible. In this context a color pattern is an i× j array of colored cells. An array in which every column and row is labeled with a different color is called maximal. One question is how many cells are needed to create a weaveable pattern that has k different colors. Obviously, this can be done with a 1×k or k×1 pattern: a single row or column with a cell for each different color. These cases, however, are degenerate and uninteresting. For maximal patterns, k is partitioned into two parts. There are k – 2 nondegenerate size combinations, given by