Remi Cocou Avohou

Remi Cocou Avohou
African Institute for Mathematical Sciences Senegal | AIMS Senegal · Priogram in Mathematics and its Applications

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16
Publications
529
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56
Citations
Introduction

Publications

Publications (16)
Preprint
The handle slide operation, originally defined for ribbon graphs, was extended to delta-matroids by I. Moffatt and E. Mphako-Bandab, who show that, using a delta-matroid analogue of handle slides, every binary delta-matroid in which the empty set is feasible can be written in a canonical form analogous to the canonical form for one-vertex maps on a...
Preprint
Using Tutte's combinatorial definition of a map we define a $\Delta$-matroid purely combinatorially and show that it is identical to Bouchet's topological definition.
Preprint
We give necessary and sufficient conditions for two matroids on the same ground set to be the upper and lower matroid of a $\Delta$-matroid.
Article
The Bollobás–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 gener...
Article
In this work we study the operations of handle slides introduced recently for delta-matroids by Iain Moffatt and Eunice Mphako-Banda. We then prove that any class of delta-matroids that is closed under handle slides is a subclass of the class of binary delta-matroids.
Preprint
O(N)$ invariants are the observables of real tensor models. We use regular colored graphs to represent these invariants, the valence of the vertices of the graphs relates to the tensor rank. We enumerate $O(N)$ invariants as $d$-regular graphs, using permutation group techniques. We also list their generating functions and give (software) algorithm...
Preprint
In this work, we study the operations of handle slides introduced recently for delta-matroids by Iain Moffatt and Eunice Mphako-Banda. We then prove that the class of binary delta-matroids is the only class of delta-matroids closed under handle slides.
Article
It is known that graphs cellularly embedded into surfaces are equivalent to ribbon graphs. In this work, we generalize this statement to broader classes of graphs and surfaces. Half-edge graphs extend abstract graphs and are useful in quantum field theory in physics. On the other hand, ribbon graphs with half-edges generalize ribbon graphs and appe...
Article
The $2$-decomposition for ribbon graphs was introduced in [Annals of Combinatorics 15 (2011), pp 675-706]. We extend this result to half-edged ribbon graphs and to rank $D$-weakly colored graphs [SIGMA 12 (2016), 030], generalizing therefore the $2$-sums and tensor products of these graphs. Using this extension for the $2$-decompositions, we provid...
Article
Full-text available
This paper is devoted to the study of renormalization of the quartic melonic tensor model in dimension (=rank) five. We review the perturbative renormalization and the computation of the one loop beta function, confirming the asymptotic freedom of the model. We then define the Connes-Kreimer-like Hopf algebra describing the combinatorics of the ren...
Article
Polynomials on stranded graphs are higher dimensional generalization of Tutte and Bollob\`as-Riordan polynomials [Math. Ann. 323, 81 (2002)]. Here, we deepen the analysis of the polynomial invariant defined on rank 3 weakly-colored stranded graphs introduced in arXiv:1301.1987 [math.CO]. We successfully find in dimension $D\geq3$ a modified Euler c...
Article
Full-text available
We provide recipe theorems for the Bollob\`as and Riordan polynomial $\mathcal{R}$ defined on classes of ribbon graphs with half-edges introduced in arXiv:1310.3708[math.GT]. We also define a generalized transition polynomial $Q$ on this new category of ribbon graphs and establish a relationship between $Q$ and $\mathcal{R}$.
Article
Full-text available
In this paper, we analyze the Bollobas and Riordan polynomial for ribbon graphs with flags introduced in arXiv:1301.1987 and prove its universality. We also show that this polynomial can be defined on some equivalence classes of ribbon graphs involving flag moves and that the new polynomial is still universal on these classes.
Article
Full-text available
The Bollobas-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 graphs called rank 3 weakly-colored stranded graphs. These graphs live in a 3D space and appear as the gluing stranded vertices with stranded edges according to a defin...
Article
The Bollobas-Riordan polynomial [Math. Ann. 323, 81 (2002)] extends the Tutte polynomial and its contraction/deletion rule for ordinary graphs to ribbon graphs. Given a ribbon graph $\cG$, the related polynomial should be computable from the knowledge of the terminal forms of $\cG$ namely specific induced graphs for which the contraction/deletion p...

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