2004/12/02 by Elvira Di Nardo, E. Di Nardo, Di Nardo, E. +2
Mathematics · #05A40 #60C05 (Primary) #Combinatorics (math.CO) #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #math.CO #math.PR #msc:05A40 #msc:60C05
paper · pdf · doi:10.48550/arxiv.math/0412054
23 pages
arxiv created 2004/12/02 · openalex publication_date 2004/12/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Extending the rigorous presentation of the classical umbral calculus given by Rota and Taylor in 1994, the so-called partition polynomials are interpreted with the aim to point out the umbral nature of the Poisson random variables. Among the new umbrae introduced, the main tool is the partition umbra that leads also to a simple expression of the functional composition of the exponential power series. Moreover a new short proof of the Lagrange inversion formula is given.