Extending the Tutte and Bollob\'as-Riordan Polynomials to Rank 3 Weakly-Colored Stranded Graphs
Abstract
The Bollob\'as-Riordan polynomial [Math. Ann. 323, 81 (2002)] is a universal polynomial invariant for ribbon graphs. We find an extension of this polynomial for a particular family of combinatorial objects, called rank 3 weakly-colored stranded graphs. Stranded graphs arise in the study of tensor models for quantum gravity in physics, and generalize graphs and ribbon graphs. We present a seven-variable polynomial invariant of these graphs, which obeys a contraction/deletion recursion relation similar to that of the Tutte and Bollob\'as-Riordan polynomials. However, it is defined on a much broader class of objects, and furthermore captures properties that are not encoded by the Tutte or Bollob\'as-Riordan polynomials.
Keywords
Cite
@article{arxiv.1301.1987,
title = {Extending the Tutte and Bollob\'as-Riordan Polynomials to Rank 3 Weakly-Colored Stranded Graphs},
author = {Remi C. Avohou and Joseph Ben Geloun and Mahouton N. Hounkonnou},
journal= {arXiv preprint arXiv:1301.1987},
year = {2022}
}
Comments
41 pages, 32 figures; improved version (published), some statements corrected