Lipids containing long polymethylene chains were among the first compounds subjected to electron diffraction structure analysis. It was only recently realized, however, that various distortions of thin lipid microcrystal plates, e.g. bends, polar group and methyl end plane disorders, etc. (1-3), restrict coherent scattering to the methylene subcell alone, particularly if undistorted molecular layers have well-defined end planes. Thus, ab initio crystal structure determination on a given single uncharacterized natural lipid using electron diffraction data can only hope to identify the subcell packing and the chain axis orientation with respect to the crystal surface. In lipids based on glycerol, for example, conformations of long chains and polar groups about the C-C bonds of this moiety still would remain unknown.One possible means of surmounting this difficulty is to investigate structural analogs of the material of interest in conjunction with the natural compound itself. Suitable analogs to the glycerol lipids are compounds based on the three configurational isomers of cyclopentane-1,2,3-triol shown in Fig. 1, in which three rotameric forms of the natural glycerol derivatives are fixed by the ring structure (4-7).
$\mathfrak{q}$-Crystal Structure on Primed Tableaux and on Signed Unimodal Factorizations of Reduced Words of Type $B$
