Chromatic polynomials of partition systems
type: Item
instance of: scholarly article
title: Chromatic polynomials of partition systems
zbMATH Open document ID: 0872.05013
DOI: 10.1016/S0012-365X(96)00245-2
author: Cristian Lenart
author: N. Ray
published in: Discrete Mathematics
publication date: 1997-09-19T00:00:00Z
review text: The authors develop a generalization of chromatic polynomials to certain set systems called partition systems (the independent subsets of a graph form a partition system where their polynomial specializes to the classical chromatic polynomial). This also generalizes the umbral chromatic polynomial in the context of the Roman-Rota umbral calculus. The authors have in mind applications to algebraic topology and formal group laws, but this paper concentrates on combinatorial aspects, proving various identities involving these polynomials and generalizations of properties of the classical chromatic polynomial. Partition systems with a group action are also considered.
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05A18
Mathematics Subject Classification ID: 05A40
Mathematics Subject Classification ID: 05E25
zbMATH DE Number: 1018531
zbMATH Keywords: chromatic polynomial
zbMATH Keywords: partition
zbMATH Keywords: set system
zbMATH Keywords: umbral
reviewed by: Albert J. Goodman
MaRDI profile type: Publication
cites work: Q4067782
cites work: On the Foundations of Combinatorial Theory. VII: Symmetric Functions through the Theory of Distribution and Occupancy
cites work: Incidence algebra antipodes and Lagrange inversion in one and several variables
cites work: Q3901604
cites work: A rational approach to Hopf rings
cites work: Q5675806
cites work: Tutte Algebras of Graphs and Formal Group Theory
cites work: Coclosure operators and chromatic polynomials.
cites work: Q4712033
cites work: Q3812261
cites work: Q3320678
cites work: On the foundations of combinatorial theory I. Theory of M�bius Functions
cites work: Q3748279
cites work: A symmetric function generalization of the chromatic polynomial of a graph
cites work: The partition polynomial of a finite set system
cites work: Q3752420
Wikidata QID: Q126591722
description: scientific article; zbMATH DE number 1018531