Name
Title | ||
|---|---|---|
A generating function that counts the combinatorial full-span sub array structure of a regular array with some applications to APL |
Abstract | ||
|---|---|---|
Using a radically new way of representing arrays, we present a formalism that expands (or decomposes) a regular array into a weighted sum of null arrays. We show that this "polynomial" expansion (1.16) exhaustively represents the regular full-span array sub structure of the original array. Full-span means full length in the dimensions used. The polynomial is a generating function whose coefficients of which count and indicate the shape of the regular full-span sub arrays of the given regular array. These results are all structural. They do not use knowledge of the particular data contents of the arrays. We apply this new decomposition to catenation and lamination and uncover some new insights into array structure.The decomposition and the algebraic results provide a unifying view and new formalism for regular multi-dimensional arrays. It has application wherever multi-dimensional arrays are used, particularly to generalized hyper cube architectures, OLAP hierarchical data structures, and array oriented languages. It subsumes some previous results. Some of these applications are indicated with their bibliography.There is a combinatorial argument on the shape vector that could generate the coefficients, but it does not give the structural insight of this approach. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1145/882067.882076 | APL |
Keywords | Field | DocType |
original array,multi-dimensional array,regular array,regular full-span sub array,array structure,generating function,regular full-span array sub,null array,regular multi-dimensional array,new formalism,new decomposition,combinatorial full-span sub array | Array data structure,Generating function,Algebraic number,Polynomial,Computer science,Algorithm,Array data type,Online analytical processing,Hierarchical database model,Hypercube | Conference |
ISBN | Citations | PageRank |
1-58113-668-4 | 1 | 0.82 |
References | Authors | |
3 | 1 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ronald I. Frank | 1 | 2 | 1.73 |