A combinatorial Hopf algebra for the boson normal ordering problem

@article{Bousbaa2015ACH,
  title={A combinatorial Hopf algebra for the boson normal ordering problem},
  author={Imad Eddine Bousbaa and Ali Chouria and Jean-Gabriel Luque},
  journal={arXiv: Combinatorics},
  year={2015}
}
In the aim to understand the generalization of Stirling numbers occurring in the bosonic normal ordering problem, several combinatorial models have been proposed. In particular, Blasiak \emph{et al.} defined combinatorial objects allowing to interpret the number of $S_{\bf{r,s}}(k)$ appearing in the identity $(a^\dag)^{r_n}a^{s_n}\cdots(a^\dag)^{r_1}a^{s_1}=(a^\dag)^\alpha\displaystyle\sum S_{\bf{r,s}}(k)(a^\dag)^k a^k$, where $\alpha$ is assumed to be non-negative. These objects are used to… 
Recent developments in combinatorial aspects of normal ordering
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In this paper, we report on recent progress concerning combinatorial aspects of normal ordering. After giving a short introduction to the history and motivation of normal ordering, we present some

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