Identities over set partitions
type: Item
instance of: scholarly article
title: Identities over set partitions
zbMATH Open document ID: 0939.05010
DOI: 10.1016/S0012-365X(98)00369-0
published in: Discrete Mathematics
publication date: 2000-07-05T00:00:00Z
review text: The author and T. H. Savits have used characteristic functions of compound nonhomogeneous Poisson processes to derive certain partition identities; see \textit{G. M. Constantine} and \textit{T. H. Savits} [SIAM J. Discrete Math. 7, No. 2, 194-202 (1994; Zbl 0804.05005)]. Here these results are generalized from the exponential case to arbitrary series by means of Faa di Bruno's formula, allowing the computation of higher-order derivatives of composite functions. Several special cases are demonstrated and, in particular, the case of the geometric series interpretable as probabilities of events associated with the gambler's ruin problem and related problems in queueing theory.
Mathematics Subject Classification ID: 05A18
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 1331470
zbMATH Keywords: combinatorial identities
zbMATH Keywords: partition identities
author: Gregory M. Constantine
reviewed by: Gerald L. Alexanderson
MaRDI profile type: Publication
cites work: Q4726256
cites work: A Stochastic Process Interpretation of Partition Identities
cites work: A Multivariate Faa di Bruno Formula with Applications
cites work: Q3709099
cites work: Q5589310
cites work: Q5544744
full work available at URL: s0012-365x(98)00369-0
OpenAlex ID: W2065476051
description: scientific article; zbMATH DE number 1331470