Abstract We show how the use of graded alphabets allows one to provide simpler proofs of some results on free monoids and free Lie algebras. We first generalize to graded alphabets the characterization of the length distributions of circular codes. We also show that the existence of a circular code with a given distribution of degrees is equivalent to the existence of an embedding of Lie algebras. We finally give a generalization to graded alphabets of the famous result of Eastman on comma free codes of odd degree.

中文翻译：

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分级字母、循环代码、自由李代数和无逗号代码

摘要 我们展示了分级字母表的使用如何允许人们提供关于自由幺半群和自由李代数的一些结果的更简单的证明。我们首先将圆形代码长度分布的特征推广到分级字母表。我们还表明，具有给定度数分布的循环码的存在等价于李代数嵌入的存在。我们最后对伊士曼在奇数无逗号代码上的著名结果的分级字母表进行了概括。