Information on some recent applications of umbral extensions to discrete mathematics

Abstract

At the first part of the paper we show how specific umbral extensions of the Stirling numbers of the second kind result in new type of Dobinski-like formulas. In the second part among others one recovers how and why Ward solution of uncountable family of extended difference calculus nonhomogeneous equations extends to Ward-Appell polynomials case . Illustrative specifications to q-calculus case and fibonomial calculus case are made explicit due to the usage of the so called upside down notation for objects of extended finite operator calculus .

14 pages

Cited by in corpus (5)

• Cobweb posets as noncommutative prefabs
• Graded posets inverse zeta matrix formula
• On natural join of posets properties and first applications
• Natural join construction of graded posets versus ordinal sum and discrete hyper boxes
• An example of algebraization of analysis and Fibonacci cobweb poset characterization