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Polynomial Sequences of Binomial Type and Path Integrals
Vladimir V. Kisil
School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
kisilv@maths.leeds.ac.uk
Annals of Combinatorics 6 (1) p.45-56 March, 2002
AMS Subject Classification: 05A40, 05A15, 58D30, 81Q30, 81R30, 81S40
Abstract:
Polynomial sequences of binomial type are a principal tool in the umbral calculus of enumerative combinatorics. We express as a path integral in the ``phase space'' . The Hamiltonian is and it produces a Schrödinger type equation for . This establishes a bridge between enumerative combinatorics and quantum field theory. It also provides an algorithm for parallel quantum computation.
Keywords: Feynman path integral, umbral calculus, polynomial sequence of binomial type, token, Schrodinger equation, propagator, wave function, cumulants, quantum computation

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