Simplices and Spectra of Graphs
نویسندگان
چکیده
I Let Tn be the set of congruence classes of simplices in Euclidean space E . The set Tn is an open manifold (also a semi-algebraic set) of dimension (n + 1)n/2. Coincidentally, a simplexT ∈ Tn is determined by the (n+1)n/2 lengths of its edges. Furthermore, the square of the volume of T ∈ Tn is a polynomial in the squares of the edgelengths. This polynomial is given by the Cayley-Menger determinant formula: V(T) = (−1) 2n( j!)n detC,
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ورودعنوان ژورنال:
- Discrete & Computational Geometry
دوره 43 شماره
صفحات -
تاریخ انتشار 2010