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Tracelet Hopf algebras and decomposition spaces

Tracelets are the intrinsic carriers of causal information in categorical rewriting systems. In this work, we assemble tracelets into a symmetric monoidal decomposition space, inducing a cocommutative Hopf algebra of tracelets. This Hopf algebra …

Concurrency Theorems for Non-linear Rewriting Theories

Sesqui-pushout (SqPO) rewriting along non-linear rules and for monic matches is well-known to permit the modeling of fusing and cloning of vertices and edges, yet to date, no construction of a suitable concurrency theorem was available. The lack 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 …