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Chromatic polynomials and bialgebras of ...

Foissy, Loïc...

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Chromatic polynomials and bialgebras of graphs by Foissy, Loïc ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	09-08-2023
Summary	The chromatic polynomial is characterized as the unique polynomial invariant of graphs, compatible with two interacting bialgebras structures: the first coproduct is given by partitions of vertices into two parts, the second one by a contraction-extraction process. This gives Hopf-algebraic proofs of Rota's result on the signs of coefficients of chromatic polynomials and of Stanley's interpretation of the values at negative integers of chromatic polynomi-als. We also give non-commutative version of this construction, replacing graphs by indexed graphs and Q[X] by the Hopf algebra WSym of set partitions.
ISBN	-
Item Type	Article
File Type	pdf
File Size	30.00 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1611.04303

Citation

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AMA 11th EditionReferences

Foissy, Loïc. Chromatic polynomials and bialgebras of graphs. Australian National University. August 09, 2023. Accessed October 02, 2025. https://online.provdatabase.com/cite/14243

APA 7th EditionReferences

Foissy, Loïc. (2023). Chromatic polynomials and bialgebras of graphs. Australian National University. https://online.provdatabase.com/cite/14243

Chicago 17th EditionReferences

Foissy, Loïc. Chromatic polynomials and bialgebras of graphs. Australian National University. 2023. https://online.provdatabase.com/cite/14243

HarvardReferences

Foissy, Loïc. (2023). Chromatic polynomials and bialgebras of graphs. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/14243. (Accessed 02 October 2025).

Harvard AustraliaReferences

Foissy, Loïc, 2023, Chromatic polynomials and bialgebras of graphs, Australian National University, viewed 02 October 2025, <https://online.provdatabase.com/cite/14243>

MLA 9th EditionWorks Cited

Foissy, Loïc. Chromatic polynomials and bialgebras of graphs. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/14243.

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