Remarks on umbral evaluations of chromatic polynomials
type: Item
instance of: scholarly article
title: Remarks on umbral evaluations of chromatic polynomials
zbMATH Open document ID: 0795.05061
DOI: 10.1016/0012-365X(94)90292-5
author: Stefano D. Sarti
published in: Discrete Mathematics
publication date: 1994-04-04T00:00:00Z
review text: The author has studied the polynomial \(\chi (u) = a_ 1u^ 1+ a_ 2u^ 2 + \cdots + a_ nu^ n\) which generalizes the concept of chromatic polynomial of graphs. It is shown that a suitable umbral evaluation \(a_ 1u_ 1+ a_ 2u_ 2 + \cdots + a_ nu_ n\) of the polynomial gives the solution of a class of coloring enumeration problems depending on a group action on the set of colors. These results are obtained using the Pólya-de Bruijn theory. Applications include proofs of several formulas for \(B_ n\), the number of partitions of an \(n\)-set.
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05A18
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 540964
zbMATH Keywords: chromatic polynomial
zbMATH Keywords: umbral evaluation
zbMATH Keywords: coloring enumeration problems
zbMATH Keywords: Pólya-de Bruijn theory
zbMATH Keywords: number of partitions
MaRDI profile type: Publication
cites work: Q3050437
cites work: Q4770409
cites work: Q3254323
cites work: Q5519913
cites work: Coclosure operators and chromatic polynomials.
cites work: The Number of Partitions of a Set
description: scientific article; zbMATH DE number 540964