Let D be a link diagram with n crossings, sA and sB its extreme states and |sAD| (resp. |sBD|) the number of simple closed curves that appear when smoothing D according to sA (resp. sB). We give a general formula for the sum |sAD| + |sBD| for a k-almost alternating diagram D, for any k, characterizing this sum as the number of faces in an appropriate triangulation of an appropriate surface with...

The asymmetric unit of the title compound, (C(4)H(10)NO)(2)[SbCl(5)], consists of two morpholinium cations in chair conformations, and a penta-chloridoanti-monate dianion with the Sb(III) ion in a slightly distorted square-pyramidal coordination environment. The morpholinium cations are connected to each other by N-H⋯O hydrogen bonds, and they link the chloride anions and the anti-monate SbCl(3...

Two novel lanthanoid thioantimonates [Sm(4)(tepa)(4)(μ-η(2),η(3)-Sb(3)S(7))(2)(μ-Sb(2)S(4))] (1, tepa = tetraethylenepentamine) and [Eu(2)(tepa)(2)(μ-SbS(3))(μ-OH)](2)(SbS(4))(OH)·H(2)O (2) were solvothermally synthesized. Compound 1 represents the only example of different types of [Sb(3)S(7)](5-) and [Sb(2)S(4)](2-) anions coexisting in the same lanthanoid thioantimonate framework, while 2 di...