超立方体的谱

The Spectra of Hypercubes

对于超立方体的谱问题，首先获得了ｎ－维超立方体Ｂｎ的特征多项式Ｐ（Ｂｎ；λ）的递推公式Ｐ（Ｂｎ＋１；λ）＝Ｐ（Ｂｎ；λ＋１）Ｐ（Ｂｎ；λ－１）．在此基础上得到了ｎ－维超立方体Ｂｎ的谱：当ｎ是奇数时，其特征值是小于或等于ｎ的所有的正奇数和所有的负奇数；当ｎ是偶数时，其特征值是小于或等于ｎ的所有的正偶数和所有的负偶数，并且它们所对应的重数（从小到大）所形成的序列恰好是杨辉三角形的第ｎ＋１行．

The spectrum of the hypercube is obtained in this paper.The spectrum of B n(n≥1) are given by all the odd (if n is odd) or even (if n is even) integers with absolute values less than or equal to n and the multiplicities of these eigenvalues are given by the values on the ( n+1) th row of the Pascal triangle.