We show the combinatorics behind the Wilcoxon-Mann-Whitney two-sample test. This yields new combinatorial proofs of recurrences for its null distribution given recently by Brus and Chang, as well as… (More)

We present two rules for generating State Machine Workflow (SMWf) nets. We prove the soundness of these rules, i.e., we show that applying these rules to an SMWf net results in an SMWf net. We also… (More)

We survey the mathematical literature on umbral calculus (otherwise known as the calculus of finite differences) from its roots in the 19th century (and earlier) as a set of “magic rules” for… (More)

We generalize to several variables Kurbanov and Maksimov's result that all linear polynomial operators can be expressed as a formal sum P 1 k=0 ak(X)D k in terms of the derivative D (or any degree… (More)

We prove the following conjecture of Narayana: there are no nontrivial dominance refinements of the Smirnov two-sample test if and only if the two sample sizes are relatively prime. We also count the… (More)

We present a new method to compute formulas for the action on monomials of a generalization of binomial approximation operators of Popoviciu type, or equivalently moments of associated discrete… (More)

Rota's Umbral Calculus uses sequences of Sheffer polynomials to count certain combinatorial objects. We review this theory and some of its generalizations in light of our computer implementation… (More)

We characterize the Sheeer sequences by a single convolution identity F (y) pn(x) = n X k=0 pk(x) pn?k(y) where F (y) is a shift-invariant operator. We then study a generalization of the notion of… (More)

We generalize to several variables Kurbanov and Maksimov’s result that all linear polynomial operators can be expressed as a formal sum ∑∞ k=0 ak(X) D k in terms of the derivative D (or any degree… (More)