On the determination of sets by their triple correlation in finite cyclic groups
| dc.creator | Keleti, Tamas | |
| dc.creator | Kolountzakis, Mihail N. | |
| dc.date | 2006-03-16 | |
| dc.date.accessioned | 2026-07-07T07:07:00Z | |
| dc.date.available | 2026-07-07T07:07:00Z | |
| dc.description | Let $G$ be a finite abelian group and $E$ a subset of it. Suppose that we know for all subsets $T$ of $G$ of size up to $k$ for how many $x \in G$ the translate $x+T$ is contained in $E$. This information is collectively called the $k$-deck of $E$. One can naturally extend the domain of definition of the $k$-deck to include functions on $G$. Given the group $G$ when is the $k$-deck of a set in $G$ sufficient to determine the set up to translation? The 2-deck is not sufficient (even when we allow for reflection of the set, which does not change the 2-deck) and the first interesting case is $k=3$. We further restrict $G$ to be cyclic and determine the values of $n$ for which the 3-deck of a subset of $\ZZ_n$ is sufficient to determine the set up to translation. This completes the work begun by Grünbaum and Moore as far as the 3-deck is concerned. We additionally estimate from above the probability that for a random subset of $\ZZ_n$ there exists another subset, not a translate of the first, with the same 3-deck. We give an exponentially small upper bound when the previously known one was $O(1\bigl / \sqrt{n})$. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0603415 | |
| dc.identifier | http://arxiv.org/abs/math/0603415 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110235 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 43A25 | |
| dc.title | On the determination of sets by their triple correlation in finite cyclic groups | |
| dc.type | text |