The spectrum of a Hamiltonian cycle (Gray code) in a Boolean n-cube is a sequence of n numbers, where the ith number is equal to the number of edges of the ith direction in the cycle. Necessary conditions for the existence of a Gray code with a given spectrum are known: all numbers are even and the sum of any k numbers is at least $2^k$, $k=1,\dots ,n$. It is proved that for all dimensions n these necessary conditions are sufficient for the existence of a Gray code with the given spectrum.

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关于 n 立方体中哈密顿循环的谱

布尔n立方体中哈密​​顿循环（格雷码）的频谱是n 个数字的序列，其中第i个数字等于循环中第i个方向的边数。已知具有给定谱的格雷码存在的必要条件：所有数都是偶数且任意k个数的和至少为$2^{克}$, $克=1,\dots ,n$. 证明了对于所有维度n这些必要条件对于给定频谱的格雷码的存在是充分的。