论文标题
从严格订单的准对称功能中重建根树
Reconstructing Rooted Trees From Their Strict Order Quasisymmetric Functions
论文作者
论文摘要
在图理论中，确定两个图是同构是一个重要且困难的问题。朝这个问题取得进展的一种方法是查找和研究区分大量图的图形不变性。斯坦利（Stanley）猜想他的色素对称功能可以区分所有树木，而这些树木尚未解决。最近，Hasebe和Tsujie引入了Stanley功能的POSET功能的类似物，称为严格的准对称函数，并证明了它区分了所有生根的树。在本文中，我们设计了一个程序，可以通过采样有限数量的项，从其严格的准对称函数中明确重建根生的树。该过程不仅提供了Hasebe和Tsujie结果的组合证明，而且还可以追踪每个根树的代表性术语，以将其与其他生根树区分开。
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.
