5 research outputs found
31th International Symposium on Theoretical Aspects of Computer Science: STACS '14, March 5th to March 8th, 2014, Lyon, France
Get PDF
The enumeration of stack polytopes and simplical clusters
Get PDFAbstractA simplicial d-cluster may be informally described as being constructed by gluing regular d-simplexes together facet-by-facet, at each stage gluing a new simplex to exactly one facet of a cluster already constructed. The equivalence classes of such clusters under rigid motions are in one-to-one correspondence with the combinatorial types of stack polytopes.In this paper we show how to enumerate simplicial d-clusters (and hence the stack polytopes), and carry out the enumeration for d=3, 4. The enumerations are performed both for even rigid motions and for all rigid motions; that is, when reflection is not allowed and also when it is. Some numerical results are given
