A. Di Bucchianico

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math.CO1995

A simpler characterization of Sheffer polynomial

Alessandro Di Bucchianico, Daniel E. Loeb

We characterize the Sheffer sequences by a single convolution identity $F^{(y)} p_{n} (x) = k = 0 \sum n p_{k} (x) p_{n - k} (y)$ where $F^{(y)}$ is a shift-invariant operator.…

math.CO1995★ 1 cited

Maple umbral calculus package

Anne Bottreau, Alessandro Di Bucchianico, Daniel E. Loeb

We are developing a Maple package of functions related to Rota's Umbral Calculus. A Mathematica version of this package is being developed in parallel.

math.CO1995

Proof of a conjecture of Narayana on dominance refinements of the Smirnov two-sample test

Alessandro Di Bucchianico, Daniel E. Loeb

We prove the following conjecture of Narayana: there are no dominance refinements of the Smirnov two-sample test if and only if the two sample sizes are relatively prime.

math.CO1995

DX-operator expansion

Alessandro Di Bucchianico, Daniel E. Loeb

We characterize those linear operators that can be expressed as a sum over k of terms of the form f_k(D) x^k and give several examples.