We study hypergraphs which are uniquely determined by their chromatic, independence and matching polynomials. B. Bollobas, L. Pebody and O. Riordan (2000) conjectured (BPR-conjecture) that almost all graphs are uniquely determined by their chromatic
polynomials. We show that for $r$-uniform hypergraphs with $r geq 3$ this is almost never the case. This disproves the analolgue of the BPR-conjecture for $3$-uniform hypergraphs. For $r =2$ this also holds for the independence polynomial, as shown by J.A. Makowsky and V. Rakita (2017), whereas for the chromatic and matching polynomial this remains open.
Experimental measurements clearly reveal the presence of bulk superconductivity in the CsPbxBi4-xTe6 (0.3=<x=<1.0) materials, i.e. the first member of the thermoelectric series of Cs[PbmBi3Te5+m], these materials have the layered orthorhombic structu
re containing infinite anionic [PbBi3Te6]- slabs separated with Cs+ cations. Temperature dependences of electrical resistivity, magnetic susceptibility, and specific heat have consistently demonstrated that the superconducting transition in CsPb0.3Bi3.7Te6 occurs at Tc=3.1K, with a superconducting volume fraction close to 100% at 1.8 K. Structural study using aberration-corrected STEM/TEM reveals a rich variety of microstructural phenomena in correlation with the Pb-ordering and chemical inhomogeneity. The superconducting material CsPb0.3Bi3.7Te6 with the highest Tc shows a clear ordered structure with a modulation wave vector of q=a*/2+ c*/1.35 on the a-c plane. Our study evidently demonstrates that superconductivity deriving upon doping of narrow-gap semiconductor is a viable approach for exploration of novel superconductors.
