N dimensional Boolean hypercubes and the goldbach conjecture
Sir: Previous experience held in this laboratory on the subject of N Dimensional Hypercubes, via quantum similarity parameters, see for example references [1 12] has started constructing Hypercubic structures in order to obtain an automatic way of graphically represent molecular set elements, while connecting them with their properties [13 19] via the Kruskal's minimal spanning tree algorithm [20] Moreover, Hypercube structure seems important in applications related to quite different fields, like N representability problem of electron distribution functions [21,22] Furthermore, some work has been also developed about the role which Hypercubes have in the definition of Boolean tagged sets [23] Such tagged sets might be also related to fuzzy sets, see for example references [24,25] On the other hand, Boolean Hypercubes have been recently used to provide a naive demonstration of the Erdos discrepancy conjecture [26] Moreover, a newly published work ofKaatz andBultheel on topological indices and other subjects related to such N dimensional polyhedra [27] demonstrates the timely andgeneral interest ofHypercube studies in mathematical chemistry. Consequently, even if Hypercube structure has been beforehand discussed in part within references [23,26] it seems interesting to develop and organize some more related characteristic properties in order to set up further possible applications. Such is the aim of this letter. Then, the mentioned previous experience and precise considerations, about the connection of Hypercubes with the development of quantum similarity, permit to write the following definitions, notes and properties about N Dimensional Hypercubes:
Journal of Mathematical Chemistry