On storing concatenable arrays

摘要

Previous studies of extendible array storage mappings (esm's) have envisioned arrays as expanding via a sequence of adjunctions of rows and/or columns. Another mechanism for array expansion is the successive (row-wise or column-wise) concatenation of already stored arrays. This type of expansion is facilitated if the addresses of positions of the resultant composite arrays can be obtained easily and systematically from the addresses of positions of the constituent arrays. A property of esm's, termed translatability, is introduced and is argued intuitively to guarantee easy concatenation of stored arrays. The class of persistent two-dimensional translatable esm's is shown to be a one-parameter family of esm's whose initial member is the familiar diagnonal pairing function. The derived explicit form of these esm's permits one to argue algorithmically that they afford one easy concatenation of stored arrays.