Quantum physics has revealed many interesting formal properties associated with the
algebra of two operators, A and B, satisfying the partial commutation relation AB-BA= 1. This …

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 …

We demonstrate that the most well-known approach to rewriting graphical structures, the
Double-Pushout (DPO) approach, possesses a notion of sequential compositions of rules …

We propose an algebraic approach to stochastic graph-rewriting which extends the classical
construction of the Heisenberg-Weyl algebra and its canonical representation on the Fock …

Sesqui-pushout (SqPO) rewriting is a variant of transformations of graph-like and other types
of structures that fit into the framework of adhesive categories where deletion in unknown …

We develop a novel method to analyze the dynamics of stochastic rewriting systems
evolving over finitary adhesive, extensive categories. Our formalism is based on the so …

Using a quantum field theory renormalization group-like differential equation, we give a new
proof of the recipe theorem for the Tutte polynomial for matroids. The solution of such an …

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 …

The concept of diagrammatic combinatorial Hopf algebras in the form introduced for
describing the Heisenberg-Weyl algebra in~\cite {blasiak2010combinatorial} is extended to …

Motivated by a question and some enumerative conjectures of Richard Stanley, we explore
the equivalence classes of words in the Weyl algebra, $\mathbf {k}\left< D, U\mid DU-UD …