\input zb-basic
\input zb-ioport
\iteman{io-port 05646269}
\itemau{Huck, Christian}
\itemti{Uniqueness in discrete tomography of Delone sets with long-range order.}
\itemso{Discrete Comput. Geom. 42, No. 4, 740-758 (2009).}
\itemab
Summary: We address the problem of determining finite subsets of Delone sets $\Lambda \subset \Bbb R^{d}$ with long-range order by $X$-rays in prescribed $\Lambda $-directions, i.e., directions parallel to nonzero interpoint vectors of $\Lambda $. Here, an $X$-ray in direction $u$ of a finite set gives the number of points in the set on each line parallel to $u$. For our main result, we introduce the notion of algebraic Delone sets $\Lambda \subset \Bbb R^{2}$ and derive a sufficient condition for the determination of the convex subsets of these sets by $X$-rays in four prescribed $\Lambda $-directions.
\itemrv{~}
\itemcc{}
\itemut{discrete tomography; discrete parallel $X$-ray; $U$-polygon; algebraic Delone set; $p$-adic valuation; cyclotomic model set}
\itemli{doi:10.1007/s00454-009-9213-z}
\end