Résumé : Tutte polynomial is a 2-variable polynomial defined on a graph which satisfies a contraction/deletion recurrence relation. This polynomial generalizes into the so-called Bollobas-Riordan (4-variable) polynomial for ribbon graphs which also satisfies a similar recurrence rule. In the recent Physics literature, there exists a growing interest for a new category of graphs called rank d stranded graphs. Such graphs encompass simple and ribbon graph structures and represent simplicial complexes in any dimension d. I will introduce a genuine 7-variable polynomial on these graph structures when restricted in rank 3 and when provided with a specific coloring. The polynomial satisfies a new contraction/cut rule. The procedure can be certainly extended in any rank.

 [Slides.pdf] [arXiv]

Dernière modification : Thursday 21 November 2024

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