For a sequence $P=(p\_n(x))\_{n=0}^{\\infty}$ of polynomials $p\_n(x)$, we study the $K$-tuple and $L$-shifted exponential lacunary generating functions $\\mathcal{G}\_{K,L}(\\lambda;x):=\\sum\_{n=0}^{\\infty}\\frac{\\lambda^n}{n!} p\_{n\\cdot …

We propose a concise stochastic mechanics framework for chemical reaction systems that allows to formulate evolution equations for three general types of data: the probability generating functions, the exponential moment generating functions and the …

The concept of diagrammatic combinatorial Hopf algebras in the form introduced for describing the Heisenberg-Weyl algebra in [Blasiak et al. 2010](https://arxiv.org/abs/1001.4964) is extended to the case of so-called rule diagrams that present graph …