Extending the Tutte and Bollobas-Riordan polynomials to rank 3 weakly coloured stranded graphs

被引：1

作者：

Avohou, Remi C. ^{[1
,2
]}

Ben Geloun, Joseph ^{[1
,3
]}

Hounkonnou, Mahouton N. ^{[1
]}

机构：

[1] Univ Abomey Calavi, ICMPA UNESCO Chair, Int Chair Math Phys & Applicat, 072BP50, Cotonou, Benin

[2] Ecole Normale Super Natitingou, BP72, Natitingou, Benin

[3] Univ Paris 13, Sorbonne Paris Cite, Inst Galilee, CNRS UMR 7030, 99 JB Clement LIPN, F-93430 Villetaneuse, France

来源：

COMBINATORICS PROBABILITY AND COMPUTING | 2022年 / 31卷 / 03期

关键词：

Graph theory; Tutte polynomial; Bollobas-Riordan polynomial; tensor models; RIBBON GRAPHS; GRAVITY;

D O I：

10.1017/S096354832100050X

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The Bollobas-Riordan (BR) polynomial [(2002), Math. Ann. 323 81] 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 coloured 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 BR polynamials. However, it is defined on a much broader class of objects, and furthermore captures properties that are not encoded by the Tutte or BR polynomials.

引用

页码：507 / 549

页数：43

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