 | Acta Crystallographica Section A Acta Crystallographica Section A FOUNDATIONS AND ADVANCES |
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![[Figure 1]](uv5014fig1mag.jpg)
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Figure 1
Geometric interpretation for the problem of finding the number of ways of combining individual Wyckoff positions of given multiplicities and arities, (Mi,Ai), adding up to a given total multiplicity and arity (M,A). In the illustration, the target vector (M,A) = (12,3), here written in row form, is denoting a point in the two-dimensional integer lattice ![[{\bb Z}^{2}]](teximages/uv5014fi25.svg){kind=small} (square lattice) in the upper-right corner. On the top, the individual vectors
(Mi,Ai) corresponding to each Wyckoff position are shown: a (2,0) red, b (2,0) green, c (2,1) blue, d (4,1) dark red, e (4,2) dark green, f (8,3) dark blue. On the bottom, their combinations adding up to
(M,A) = (12,3) are shown, with vectors composed in reverse lexicographic order. Other possible combinations, in which only the order of the vectors are changed, are not shown. However, all lattice points which can be reached by any possible combinations of vectors are highlighted as open circles instead of filled ones. To see the full graph one has to invert the depicted half of it in the point (6, 1.5). In this interpretation the problem becomes a special case of a lattice path enumeration problem with the set of steps governed by the Wyckoff multiplicities and arities for a given choice of space-group symmetry. |
![[Figure 1]](uv5014fig1.jpg)
| FOUNDATIONS ADVANCES |
ISSN: 2053-2733
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