The history of Tutte–Whitney polynomials

Graham Farr

doi:10.1201/9780429161612-34

The history of Tutte–Whitney polynomials

Graham Farr

Department of Data Science & AI

Research output: Chapter in Book/Report/Conference proceeding › Chapter (Book) › Research › peer-review

Abstract

This chapter covers the history of Tutte–Whitney polynomials, mainly through commentary on the early papers on the topic. It focuses particularly on the following:
Notation and definitions used in the seminal papers.
Whitney, early 1930s: his papers and thesis on his rank generating function.
Tutte, 1947–1967: his papers and thesis on the Tutte polynomial.
Potts, 1952: his papers and thesis on the Potts model partition function.
Zykov's early work on related polynomials, 1949 and 1964.
Further generalizations, abstractions, interpretations of evaluations, and links to other fields, in the late 1960s and early 1970s.
Unexpectedly early appearances of many graph polynomial properties.

Original language	English
Title of host publication	Handbook of the Tutte Polynomial and Related Topics
Editors	Joanna Ellis-Monaghan, Iain Moffatt
Place of Publication	Boca Raton FL USA
Publisher	CRC Press
Chapter	34
Pages	623-668
Number of pages	46
Edition	1st
ISBN (Electronic)	9780429161612
ISBN (Print)	9781482240627, 9781032231938
DOIs	https://doi.org/10.1201/9780429161612-34
Publication status	Published - 2022

Keywords

Tutte polynomial
Tutte-Whitney polynomial
Whitney rank generating function
chromatic polynomial
graph polynomial
graph
matroid
Whitney
Tutte
Potts
Zykov
enumeration
history of mathematics

Access to Document

10.1201/9780429161612-34

Cite this

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title = "The history of Tutte–Whitney polynomials",

abstract = "This chapter covers the history of Tutte–Whitney polynomials, mainly through commentary on the early papers on the topic. It focuses particularly on the following:Notation and definitions used in the seminal papers.Whitney, early 1930s: his papers and thesis on his rank generating function.Tutte, 1947–1967: his papers and thesis on the Tutte polynomial.Potts, 1952: his papers and thesis on the Potts model partition function.Zykov's early work on related polynomials, 1949 and 1964.Further generalizations, abstractions, interpretations of evaluations, and links to other fields, in the late 1960s and early 1970s.Unexpectedly early appearances of many graph polynomial properties.",

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KW - Potts

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