$c_2$ invariants of recursive families of graphs

Chorney, Wesley; Yeats, Karen

doi:10.4171/aihpd/72

c_{2}

invariants of recursive families of graphs

Chorney, Wesley ; Yeats, Karen

Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 2, pp. 289-311.

Résumé

The $c_{2}$ invariant, defined by Schnetz in [17], is an arithmetic graph invariant created towards a better understanding of Feynman integrals.

This paper looks at some graph families of interest, with a focus on decompleted toroidal grids. Specifically, the $c_{2}$ invariant for $p = 2$ is shown to be zero for all decompleted non-skew toroidal grids. We also calculate $c_{2}^{(2)} (G)$ for $G$ a family of graphs called X-ladders. Finally, we show these methods can be applied to any graph with a recursive structure, for any fixed $p$ .

Accepté le : 2017-05-12
Publié le : 2019-03-20

MR Zbl

DOI : 10.4171/aihpd/72

Classification : 05-XX, 12-XX, 81-XX
Mots-clés :

c_{2}

invariants, recursive families of graphs, Kirchhoff polynomials, toroidal grids, spanning forest polynomials

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     author = {Chorney, Wesley and Yeats, Karen},
     title = {$c_2$ invariants of recursive families of graphs},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {289--311},
     volume = {6},
     number = {2},
     year = {2019},
     doi = {10.4171/aihpd/72},
     mrnumber = {3950656},
     zbl = {1414.05152},
     language = {en},
     url = {https://www.numdam.org/articles/10.4171/aihpd/72/}
}

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Chorney, Wesley; Yeats, Karen. $c_2$ invariants of recursive families of graphs. Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 2, pp. 289-311. doi : 10.4171/aihpd/72. https://www.numdam.org/articles/10.4171/aihpd/72/

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