A vertex-weighted tutte symmetric function, and constructing graphs with equal chromatic symmetric function
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This paper introduces a vertex-weighted version of the Tutte symmetric function XB and shows that this function admits a deletion-contraction relation, and gives several new methods for constructing nonisomorphic graphs with equal chromatic asymmetric function.Abstract:
This paper has two main parts. First, we consider the Tutte symmetric function XB, a generalization of the chromatic symmetric function. We introduce a vertex-weighted version of XB and show that this function admits a deletion-contraction relation. We also demonstrate that the vertex-weighted XB admits spanning-tree and spanning-forest expansions generalizing those of the Tutte polynomial by connecting XB to other graph functions. Second, we give several methods for constructing nonisomorphic graphs with equal chromatic and Tutte symmetric functions, and use them to provide specific examples.read more
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Journal ArticleDOI
Extended chromatic symmetric functions and equality of ribbon Schur functions
TL;DR: A general inclusion-exclusion relation is proved for the extended chromatic symmetric function of a weighted graph, which specializes to (extended) $k$-deletion, and two methods to obtain numerous new bases from weighted graphs for the algebra of symmetric functions are given.
Marked graphs and the chromatic symmetric function
TL;DR: It is proved that proper trees of diameter at most 5 can be reconstructed from its chromatic symmetric function of a graph in the star-basis of symmetric functions.
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A complete multipartite basis for the chromatic symmetric function
Logan Crew,Sophie Spirkl +1 more
TL;DR: It is shown that the coefficients of the chromatic and Tutte symmetric functions of a graph G when expanded in the r-basis enumerate certain intersections of partitions of V(G)$ into stable sets.
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Extended chromatic symmetric functions and equality of ribbon Schur functions
TL;DR: In this article, a general inclusion-exclusion relation for the extended chromatic symmetric function of a weighted graph, which specializes to (extended) $k$-deletion, was proved, and two methods to obtain numerous new bases from weighted graphs for the algebra of symmetric functions.
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Reconstructing Rooted Trees From Their Strict Order Quasisymmetric Functions
TL;DR: In this article, the authors proposed a procedure to explicitly reconstruct a rooted tree from its strict order quasisymmetric function by sampling a finite number of terms from the graph.
References
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Book
Symmetric functions and Hall polynomials
TL;DR: In this paper, the characters of GLn over a finite field and the Hecke ring of GLs over finite fields have been investigated and shown to be symmetric functions with two parameters.
Journal ArticleDOI
A Symmetric Function Generalization of the Chromatic Polynomial of a Graph
TL;DR: In this paper, the authors consider the expansion of a finite graph G with d vertices in terms of various symmetric function bases, such as partitions of the vertices into stable subsets, the Mobius function of the lattice of contractions of G, and the structure of the acyclic orientations of G.
Journal ArticleDOI
Split graphs
TL;DR: The main topics of this article are split graphs, their degree sequences, and the place of these "split partitions" at the top of the partially ordered set of graphic partitions.
Book ChapterDOI
Graph Polynomials and Their Applications I: The Tutte Polynomial
TL;DR: A survey of graph polynomials can be found in this article, with a focus on the Tutte polynomial and a selection of closely related graphs such as the chromatic, flow, reliability, and shelling polynoms.
Related Papers (5)
A Vertex-Weighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function
Logan Crew,Sophie Spirkl +1 more