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arXiv · 1504.07165

Polynomial Invariants for Arbitrary Rank $D$ Weakly-Colored Stranded Graphs

Remi Cocou Avohou
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Abstract

Polynomials on stranded graphs are higher dimensional generalization of Tutte and Bollob\'as-Riordan polynomials [Math. Ann. 323 (2002), 81-96]. Here, we deepen the analysis of the polynomial invariant defined on rank 3 weakly-colored stranded graphs introduced in arXiv:1301.1987. We successfully find in dimension $D\geq3$ a modified Euler characteristic with $D-2$ parameters. Using this modified invariant, we extend the rank 3 weakly-colored graph polynomial, and its main properties, on rank 4 and then on arbitrary rank $D$ weakly-colored stranded graphs.

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BibTeXRIS

Remi Cocou Avohou. 2015-04-27. Polynomial Invariants for Arbitrary Rank $D$ Weakly-Colored Stranded Graphs. https://doi.org/10.3842/sigma.2016.030

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