论文标题
广义色彩功能
Generalized chromatic functions
论文作者
论文摘要
我们为边分区的挖掘物定义了顶点，该绘制统一了p分区理论和图形的正确顶点色。我们使用顶点色来定义广义的色度函数，该功能合并了图形的色度对称和准对称函数，并生成了P分区的功能。此外，在通勤和非交通变量中，对称和准对称函数的许多经典基础可以被视为我们广义色彩函数的特殊情况。我们还为我们的功能建立了产品和合并公式。此外，我们在非公共变量中构建了R Quasisymmmetric函数的新型HOPF代数，并应用我们的功能来确认其HOPF结构，并为其建立自然基础。
We define vertex-colourings for edge-partitioned digraphs, which unify the theory of P-partitions and proper vertex-colourings of graphs. We use our vertex-colourings to define generalized chromatic functions, which merge the chromatic symmetric and quasisymmetric functions of graphs and generating functions of P-partitions. Moreover, numerous classical bases of symmetric and quasisymmetric functions, both in commuting and noncommuting variables, can be realized as special cases of our generalized chromatic functions. We also establish product and coproduct formulas for our functions. Additionally, we construct the new Hopf algebra of r-quasisymmetric functions in noncommuting variables, and apply our functions to confirm its Hopf structure, and establish natural bases for it.
