论文标题
扩展的色素对称函数和丝带Schur函数的平等
Extended chromatic symmetric functions and equality of ribbon Schur functions
论文作者
论文摘要
我们证明了加权图的扩展色度对称函数的一般包含 - 排斥关系，该关系专门用于（扩展）$ k $ - 删除，我们提供了两种方法，可以从对称函数代数的加权图中获取许多新基础。 此外，当两个加权路径具有相等的扩展色对称函数时，我们通过证明这等同于相等的色带Schur函数的分类来进行分类。后一种分类取决于组成的操作组成，我们将其推广到图形的组成。然后，我们应用概括以获得无限的加权图家族，其成员具有相等的延长色素对称函数。
We prove a general inclusion-exclusion relation for the extended chromatic symmetric function of a weighted graph, which specializes to (extended) $k$-deletion, and we give two methods to obtain numerous new bases from weighted graphs for the algebra of symmetric functions. Moreover, we classify when two weighted paths have equal extended chromatic symmetric functions by proving this is equivalent to the classification of equal ribbon Schur functions. This latter classification is dependent on the operation composition of compositions, which we generalize to composition of graphs. We then apply our generalization to obtain infinitely many families of weighted graphs whose members have equal extended chromatic symmetric functions.
