On the cut-complexes of the 5-cube
A cut-complex of the d-cube \(c^ d\) is the complex of faces of \(c^ d\) to one side of a hyperplane which cuts it (this is not quite the definition of the paper under review, but does seem to be the actual usage). An exterior edge of a cut-complex C joins a vertex of C to a vertex of the complementary cut-complex, and a cut of \(c^ d\) consists of the exterior edges of some cut-complex. The minimal number of cuts needed to cover the edges of \(c^ d\) is the cut-number \(k(c^ d)\). It is shown here that \(k(c^ 4)=4\); moreover, all general sections of \(c^ 4\) are found. Further, all cut-complexes of \(c^ 5\) are described by implementation of a computer program. Finally, the role of stellar subdivision and its inverse in the construction of a polytope from a simplex are investigated for the sections of \(c^ 4\).
scientific article; zbMATH DE number 4131164