超稳定张拉整体结构与 Colin de Verdière 数 $ν$
Super Stable Tensegrities and the Colin de Verdière Number $ν$
AI总结：
本文建立了多重图可实现为超稳定张拉整体的最大维数与谱图论中Colin de Verdière数ν的精确关系，并由此给出三维超稳定张拉整体多重图的组合刻画。
摘要：
Connelly 于 1982 年引入的超稳定张拉整体是一种全局刚性的离散结构，由刚性杆或支柱通过受拉缆索连接而成。本文证明了多重图能够实现为超稳定张拉整体的最大维数与谱图论中的 Colin de Verdière 数 $ν$ 之间的精确关系。作为推论，我们得到了能够实现为三维超稳定张拉整体的多重图的组合刻画。
英文摘要：
A super stable tensegrity introduced by Connelly in 1982 is a globally rigid discrete structure made from stiff bars or struts connected by cables with tension. In this paper we show an exact relation between the maximum dimension that a multigraph can be realized as a super stable tensegrity and Colin de Verdière number~$ν$ from spectral graph theory. As a corollary we obtain a combinatorial characterization of multigraphs that can be realized as 3-dimensional super stable tensegrities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
