Publications

2024

1. AC

   Planar Binary Trees, Noncrossing Partitions and the Operator-Valued S-Transform

   Kurusch Ebrahimi-Fard and Timothé Ringeard

   Annals of Combinatorics, Sep 2024

   Abs arXiv Bib

   We revisit the twisted multiplicativity property of Voiculescu’s S-transform in the operator-valued setting, using a specific bijection between planar binary trees and noncrossing partitions.

   @article{ER24Stransform,
     author = {Ebrahimi-Fard, Kurusch and Ringeard, Timothé},
     journal = {Annals of Combinatorics},
     title = {Planar Binary Trees, Noncrossing Partitions and the Operator-Valued S-Transform},
     year = {2024},
     month = sep,
     url = {https://link.springer.com/article/10.1007/s00026-024-00730-1},
     selected = false,
     bibtex_show = true,
   }

2. PREPRINT

   A post-group theoretic perspective on the operator-valued S-transform in free probability

   Kurusch Ebrahimi-Fard and Timothé Ringeard

   arXiv preprint arXiv:2402.16450, Dec 2024

   Abs arXiv Bib

   We investigate the algebraic structure underlying Voiculescu’s S-transform in the setting of operator-valued free probability. We show that its twisted factorisation property gives rise to post-groups, crossed morphisms, as well as pre- and post-Lie algebras.

   @article{ER24postgroup,
     author = {Ebrahimi-Fard, Kurusch and Ringeard, Timothé},
     journal = {arXiv preprint arXiv:2402.16450},
     title = {A post-group theoretic perspective on the operator-valued S-transform in free probability},
     year = {2024},
     month = dec,
     url = {https://arxiv.org/abs/2402.16450},
     selected = false,
     bibtex_show = true,
   }