Indecomposable Tilings of the Integers with Exponentially Long Periods

@article{Steinberger2005IndecomposableTO,
title={Indecomposable Tilings of the Integers with Exponentially Long Periods},
author={John P. Steinberger},
journal={Electr. J. Comb.},
year={2005},
volume={12}
}

Let A be a finite multiset of integers. A second multiset of integers T is said to be an A-tiling of level d if every integer can be expressed in exactly d ways as the sum of an element of A and of an element of T . The set T is indecomposable if it cannot be written as the disjoint union of two proper subsets that are also A-tilings. In this paper we show how to construct indecomposable tilings that have exponentially long periods. More precisely, we give a sequence of multisets (Ak)k=1 such… CONTINUE READING