2,069 research outputs found
Betti numbers of Stanley--Reisner rings with pure resolutions
Let be simplicial complex and let denote the
Stanley--Reisner ring corresponding to . Suppose that has a
pure free resolution. Then we describe the Betti numbers and the
Hilbert--Samuel multiplicity of in terms of the --vector of
. As an application, we derive a linear equation system and some
inequalities for the components of the --vector of the clique complex of an
arbitrary chordal graph. As an other application, we derive a linear equation
system and some inequalities for the components of the --vector of
Cohen--Macaulay simplicial complexes.Comment: 18 pages, better introduction, ask for feedback before submissio
The Theory of Bonds: A New Method for the Analysis of Linkages
In this paper we introduce a new technique, based on dual quaternions, for
the analysis of closed linkages with revolute joints: the theory of bonds. The
bond structure comprises a lot of information on closed revolute chains with a
one-parametric mobility. We demonstrate the usefulness of bond theory by giving
a new and transparent proof for the well-known classification of
overconstrained 5R linkages.Comment: more detailed explanations and additional reference
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