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Matiyasevich Formula for Chromatic and Flow Polynomials and Feynman Amplitudes

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Abstract

Matiyasevich formula which expresses the chromatic polynomial of an arbitrary graph through a linear combination of flow polynomials of subgraphs of the original graph is generalized by using the Feynman amplitudes technique. The article presents a formula expressing a flow polynomial through a linear combination of chromatic polynomials of constricted graphs. This proof is obtained by using the Feynman amplitudes technique. A simple proof of Matiyasevich formula and its consequences are derived by using the same technique.

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Funding

The work of the first author has been supported by the Kazan Federal University Strategic Academic Leadership Program (‘‘PRIORITY-2030’’). The work of the second author was supported by the Basis foundation, the grant Leader (Math) 20-7-1-21-4.

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Correspondence to E. Yu. Lerner or S. A. Mukhamedjanova.

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(Submitted by E. A. Turilova)

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Lerner, E.Y., Mukhamedjanova, S.A. Matiyasevich Formula for Chromatic and Flow Polynomials and Feynman Amplitudes. Lobachevskii J Math 43, 3552–3561 (2022). https://doi.org/10.1134/S1995080222150185

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  • DOI: https://doi.org/10.1134/S1995080222150185

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