- ON A GENERALIZED APERIODIC PERFECT MAP
- KIM, SANG-MOK ;
- Communications of the Korean Mathematical Society, volume 20, issue 4, 2005, Pages 685~693
- DOI : 10.4134/CKMS.2005.20.4.685

Abstract

An aperiodic perfect map(APM) is an array with the property that every array of certain size, called a window, arises exactly once as a contiguous subarray in the array. In this article, we deal with the generalization of APM in higher dimensional arrays. First, we reframe all known definitions onto the generalized n-dimensional arrays. Next, some elementary known results on arrays are generalized to propositions on n-dimensional arrays. Finally, with some devised integer representations, two constructions of infinite family of n-dimensional APMs are generalized from known 2-dimensional constructions in [7].