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Reconstructing Infinite Sets of Integers

✍ Scribed by Dieter Rautenbach; Eberhard Triesch

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 118 KB
Volume: 99
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2002.3271

No coin nor oath required. For personal study only.

✦ Synopsis

For a set of integers A Z and k51 the k-deck of A is the function d A;k defined on sets S of k integers by

Our main result is that for k53; a set for which the k-deck only takes finite values is determined up to translation by its k-deck and one finite non-zero value of its ðk À 1Þdeck. This generalizes a result of Radcliffe and Scott (Electron. J. Combin. 6 (1999), R20) which proved a weaker form of this statement for k ¼ 3: In order to establish this result, we generalize Kelly's Lemma for finite graphs to infinite sets of integers.

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