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## Publications

Publications (16)

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...

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.

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.

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...

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.

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...

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.

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...

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...

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...

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...

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 $\mathcal{R}$.

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.

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...

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...