自由 Novikov 代数与装饰多重指标的 Hopf 代数
Free Novikov algebras and the Hopf algebra of decorated multi-indices
AI总结：
本文为装饰多重指标 Hopf 代数提出基于容许割的余积组合公式，并利用覆盖子森林概念证明无装饰多重指标的提取-收缩余积公式。
摘要：
我们为近期文献中出现的装饰多重指标 Hopf 代数中的余积提出了一种组合公式，该代数可简要描述为由装饰集合生成的自由 Novikov 代数的包络代数的分次对偶。与有根森林的 Hopf 代数类似，该公式可用容许割来表示。我们还利用覆盖子森林的适当概念，证明了无装饰多重指标的提取-收缩余积的组合公式。
英文摘要：
We propose a combinatorial formula for the coproduct in a Hopf algebra of decorated multi-indices that recently appeared in the literature, which can be briefly described as the graded dual of the enveloping algebra of the free Novikov algebra generated by the set of decorations. Similarly to what happens for the Hopf algebra of rooted forests, the formula can be written in terms of admissible cuts. We also prove a combinatorial formula for the extraction-contraction coproduct for undecorated multi-indices, in terms of a suitable notion of covering subforest.
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。
