98-562 Kisil V.V.
Polynomial Sequences of Binomial Type and Path Integrals (18K, LATeX2e) Aug 12, 98
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Abstract. Polynomial sequences $p_n(x)$ of binomial type are a principal tool in the umbral calculus of enumerative combinatorics. We express $p_n(x)$ as a \emph{path integral} in the ``phase space'' $\Space{N}{} \times [-\pi,\pi]$. The Hamiltonian is $h(\phi)=\sum_{n=0}^\infty p_n'(0)/n! \, e^{in\phi}$ and it produces a Schrodinger type equation for $p_n(x)$. This establishes a bridge between enumerative combinatorics and quantum field theory.

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