由严格阶拟对称函数重构有根树
Reconstructing Rooted Trees From Their Strict Order Quasisymmetric Functions
摘要：
判定两个图是否同构是图论中的一个重要而又困难的问题。解决这个问题的一种方法是找到和研究区分大类图的图不变量。斯坦利承认，他的色对称函数区分所有的树，这一直没有解决。最近，Hasebe和Tsujie在偏序集上引入了Stanley函数的一个类似物，称为严格序拟对称函数，并证明了它能区分所有的有根树。在本文中，我们设计了一个程序，显式重建一个有根树从严格的顺序准对称函数采样有限数量的条款。该过程不仅提供了Hasebe和Tsujie的结果的组合证明，而且还追踪了每个根树的代表项，以区别于其他有根树。
英文摘要：
Determining whether two graphs are isomorphic is an important and difficult problem in graph theory. One way to make progress towards this problem is by finding and studying graph invariants that distinguish large classes of graphs. Stanley conjectured that his chromatic symmetric function distinguishes all trees, which has remained unresolved. Recently, Hasebe and Tsujie introduced an analogue of Stanley's function for posets, called the strict order quasisymmetric function, and proved that it distinguishes all rooted trees. In this paper, we devise a procedure to explicitly reconstruct a rooted tree from its strict order quasisymmetric function by sampling a finite number of terms. The procedure not only provides a combinatorial proof of the result of Hasebe and Tsujie, but also tracks down the representative terms of each rooted tree that distinguish it from other rooted trees.
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。
