- 98-562 Kisil V.V.
- Polynomial Sequences of Binomial Type and Path Integrals
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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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