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Compositionality of Rewriting Rules with Conditions

We extend the notion of compositional associative rewriting as recently studied in the rule algebra framework literature to the setting of rewriting rules with conditions. Our methodology is category-theoretical in nature, where the definition of …

Explicit formulae for all higher order exponential lacunary generating functions of Hermite polynomials

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 …

Combinatorics of chemical reaction systems

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 algebras of graph rewriting

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 …