Analytic combinatorics aims to enable precise quantitative predictions of the properties of
large combinatorial structures. The theory has emerged over recent decades as essential …

Commutation Relations, Normal Ordering, and Stirling Numbers Page 1 Commutation
Relations, Normal Ordering, and Stirling Numbers Toufik Mansour • Matthias Schork Mansour • …

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 …

We discuss a general combinatorial framework for operator ordering problems by applying it
to the normal ordering of the powers and exponential of the boson number operator. The …

We construct explicit representations of the Heisenberg–Weyl algebra [P, M]= 1 in terms of
ladder operators acting in the space of Sheffer-type polynomials. Thus we establish a link …

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 …

We consider the numbers arising in the problem of normal ordering of expressions in boson
creation a† and annihilation a operators ([a, a†]= 1)⁠. We treat a general form of a boson …

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 …