Parallelogram substring scale: Difference between revisions

Inthar (talk | contribs)
Inthar (talk | contribs)
Line 14: Line 14:
* <math>\{\mathbf{a} + i\mathbf{v} + j\mathbf{w}\}_{(i,j) \in [n]_0 \times [m-2]_1}</math> is a (possibly empty) parallelogram where rows are traversed fully
* <math>\{\mathbf{a} + i\mathbf{v} + j\mathbf{w}\}_{(i,j) \in [n]_0 \times [m-2]_1}</math> is a (possibly empty) parallelogram where rows are traversed fully
* <math>\{\mathbf{a} + i\mathbf{v} + (m-1)\mathbf{w}\}_{i=0}^{b}</math> is a (nonempty) prefix of the last row
* <math>\{\mathbf{a} + i\mathbf{v} + (m-1)\mathbf{w}\}_{i=0}^{b}</math> is a (nonempty) prefix of the last row
* '''v''' and '''w''' are the generator and offset
* '''v''' is called the ''row generator''.


This concept generalizes in the obvious way to arbitrary rank ''d'' (where each (''d'' - 1)-dimensional "hyperrow" is traversed lexicographically, and the first and last hyperrows must be a suffix resp. prefix of such a traversal). In this case the property is called the '''parallelotope substring property'''.
This concept generalizes in the obvious way to arbitrary rank ''d'' (where each (''d'' - 1)-dimensional "hyperrow" is traversed lexicographically, and the first and last hyperrows must be a suffix resp. prefix of such a traversal). In this case the property is called the '''parallelotope substring property'''.