TY - JOUR
T1 - Discrete Tomography of Mathematcal Quasicrystals
T2 - A Primer
AU - Huck, Christian
AU - Baake, Michael
AU - Langfeld, Barbara
AU - Gritzmann, Peter
AU - Lord, Katja
PY - 2005/7/1
Y1 - 2005/7/1
N2 - This text is a report on work progress. We introduce the class of cyclotomic model sets (mathematical quasicrystals) Λ ⊂ Z [ξn], where Z [ξn] is the ring of integers in the nth cyclotomic field Q (ξn), and discuss the corresponding decomposition, consistency and reconstruction problems of the discrete tomography of these sets. Our solution of the so-called decomposition problem also applies to the case of the square lattice Z2 = Z [ξ4], which corresponds to the classical setting of discrete tomography.
AB - This text is a report on work progress. We introduce the class of cyclotomic model sets (mathematical quasicrystals) Λ ⊂ Z [ξn], where Z [ξn] is the ring of integers in the nth cyclotomic field Q (ξn), and discuss the corresponding decomposition, consistency and reconstruction problems of the discrete tomography of these sets. Our solution of the so-called decomposition problem also applies to the case of the square lattice Z2 = Z [ξ4], which corresponds to the classical setting of discrete tomography.
KW - Consistency problem
KW - cyclomatic model set
KW - decomposition problem
KW - discrete tomography
KW - reconstruction problem
UR - https://www.scopus.com/pages/publications/34247176350
U2 - 10.1016/j.endm.2005.05.062
DO - 10.1016/j.endm.2005.05.062
M3 - Article
AN - SCOPUS:34247176350
SN - 1571-0653
VL - 20
SP - 179
EP - 191
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
ER -