Due to the complexity and continuing evolution of such systems, it is desirable to maintain as much software controllability in the field as possible. Time to market can also be improved by reducing the amount of hardware design. This paper describes an architecture based on clusters of embedded "workhorse" processors which can be dynamically harnessed in real time to support a wide range of computational tasks. Low-power processors and memory are important ingredients in such a highly parallel environment.
A kℓ-subset partition, or (k, ℓ)-subpartition, is a kℓ-subset of an n-set that is partitioned into ℓ distinct classes, each of size k. Two (k, ℓ)-subpartitions are said to t-intersect if they have at least t classes in common. In this paper, we prove an Erdős-Ko-Rado theorem for intersecting families of (k, ℓ)-subpartitions. We show that for n ≥ kℓ, ℓ ≥ 2 and k ≥ 3, the largest 1-intersecting family contains at most-subpartitions, and that this bound is only attained by the family of (k, ℓ)-subpartitions with a common fixed class, known as the canonical intersecting family of (k, ℓ)-subpartitions. Further, provided that n is sufficiently large relative to k, ℓ and t, the largest t-intersecting family is the family of (k, ℓ)-subpartitions that contain a common set of t fixed classes.
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