Robert, My reply is not exactly directed at nor relevant to your question, but having recently thought at some length about how to explain Hui's essay I concluded that understanding the arrays R and I is foremost. Focusing on the rows of R and I, one row at a time, clarifies their purpose best for me.
I contains 81 rows. Each row corresponds to an element of the 9x9 grid i. 9 9 and contains the indices of the 21 distinct cells (including intself) for which it is constrained to be unique (there are 21, not 27, distinct cells because some cells would be repeated in a list of 27). The array j is used to construct the parts of I that involve 9-cell boxes, referred to as b by Hui. R contains 27 rows. Each row contains the cell indices of either a 9-cell box, a row, or a column, of the 9x9 grid i. 9 9 . The array j is used to construct the first 9 rows of R which contain indices of 9-cell boxes. -- (B=) ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
