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

Polynomials on stranded graphs are higher dimensional generalization of Tutte and Bollobás–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.