201 citations · 2.4k across the 113 of their papers we have counts for
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Eight times four bialgebras of hypergraphs, cointeractions, and chromatic polynomials
Kurusch Ebrahimi-Fard, Gunnar Fløystad
We consider the bialgebra of hypergraphs, a generalization of Schmitt's Hopf algebra of graphs, and show it has a cointeracting bialgebra. So one has a double bialgebra in the sens…
Algebraic groups in non-commutative probability theory revisited
Ilya Chevyrev, Kurusch Ebrahimi-Fard, Frédéric Patras
The role of coalgebras as well as algebraic groups in non-commutative probability has long been advocated by the school of von Waldenfels and Schürmann. Another algebraic approach…
Signatures of graphs for bicommutative Hopf algebras
Diego Caudillo, Joscha Diehl, Kurusch Ebrahimi-Fard +1
This article approaches the counting of subgraphs, in terms of signature-type functionals defined over combinatorial Hopf algebras of graphs. Well-known algebraic identities that a…
Algebraic aspects of connections: from torsion, curvature, and post-Lie algebras to Gavrilov's double exponential and special polynomials
M. J. H. Al-Kaabi, K. Ebrahimi-Fard, D. Manchon +1
Understanding the algebraic structure underlying a manifold with a general affine connection is a natural problem. In this context, A. V. Gavrilov introduced the notion of framed L…
Shifted Substitution in Non-Commutative Multivariate Power Series with a View Toward Free Probability
Kurusch Ebrahimi-Fard, Frédéric Patras, Nikolas Tapia +1
We study a particular group law on formal power series in non-commuting variables induced by their interpretation as linear forms on a suitable graded connected word Hopf algebra.…