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

Abstract

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 $D\ge 3$ 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.

Basic definitions overlap with arXiv:1301.1987

References in corpus (3)

• Extending the Tutte and Bollobás-Riordan Polynomials to Rank 3 Weakly-Colored Stranded Graphs
• On terminal forms for topological polynomials for ribbon graphs: The $N$-petal flower
• Recipe theorems for polynomial invariants on ribbon graphs with half-edges

Cited by in corpus (4)

• Extending the Tutte and Bollobás-Riordan Polynomials to Rank 3 Weakly-Colored Stranded Graphs
• A multidimensional generalization of Symanzik polynomials
• The expansion of polynomial invariants for $2$-decompositions of generalized graphs
• Embedding Half-Edge Graphs in Punctured Surfaces