Abstract
For both highern andI i ≧1 spin clusters, combinatorics provides powerful arguments with which to investigate the substructural forms of cluster spin algebras; this is especially so for SO(3) ×l n symmetries for 12≦n≦60 wherex [λ](.) character tabulations become extensive. Bijective enumerative mappings over the combinatorialp-tuples (number partitions) afford insight into the general functionf(p,n) as well as into {|IM(I 1−I n [λ]〉}M-structure of spin algebras, even where the full details of the explicitx [λ]() (l n ) characters are not readily available. Both simply-reducible and higher aspects ofl n -inner tensor product (ITP) algebras are derived from dimensionality considerations, as part of combinatorial hooklength formalisms for\(\chi _{(1^n )}^{[\lambda ]} \). TheI i ≦3/2 forms of [A] n clusters forn≦20, (forp≦3, 4) of multiple-quantum NMR (MQ-NMR) are considered here as part of current interest in giant cage-clusters. In addition, the SU2 substructural hierarchy over Liouville space is derived for [A]20(l n ) (I i =1/2) spin cluster of the cage-cluster molecule dodecahedrane; aspects ofI i =1 spin cluster over {|IM (...)〉} space are derived as high temperature model of the exo-cage of [H2O]+ @[H2O]20 cluster ion; 20-fold higher-I i lusters provide models for M @M20 metal-clusters and further applications ofl 20-number partitions.
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Temme, F.P., Colpa, J.P. Symmetry substructures for MQ-NMR of [A]20 spin clusters of dodecahedranes, [13CH]20 or [13CD]20, metallic M @M20 and [H2O]+ @[H2O]20 exo-cage cluster molecules and their higher-n SO(3) ×l n spin algebras, within the context of mapping,l n -ITP algebras and number partitions. Z Phys D - Atoms, Molecules and Clusters 25, 275–284 (1993). https://doi.org/10.1007/BF01426891
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DOI: https://doi.org/10.1007/BF01426891