Recursive initial value problems for Sheffer sequences
type: Item
instance of: scholarly article
title: Recursive initial value problems for Sheffer sequences
zbMATH Open document ID: 0944.05004
DOI: 10.1016/S0012-365X(98)00376-8
author: Heinrich Niederhausen
published in: Discrete Mathematics
publication date: 2000-09-24T00:00:00Z
review text: The combinatorial problem addressed in this paper is the enumeration of certain lattice paths. The paths of interest are those which take unit steps in the North and East directions and have weighted left turns (East followed by North). Furthermore, such paths are restricted to lie either entirely above or entirely below a line of positive slope. Each of these latter cases leads to a different recursively defined initial value problem which is solved using tools from finite operator calculus. Although the article is self-contained, the non-expert may wish to consult one or both of the following: \textit{H. Niederhausen} [``Lattice path enumeration and umbral calculus'', in N. Balakrishnan (ed.), Advances in combinatorial methods and applications to probability and statistics, Birkhäuser, Boston, 15-27 (1997; Zbl 0880.05003)] and \textit{G.-C. Rota}, \textit{D. Kahaner} and \textit{A. Odlyzko} [On the foundations of combinatorial theory. VIII: Finite operator calculus, J. Math. Anal. Appl. 42, 684-760 (1973; Zbl 0267.05004)].
reviewed by: Jennifer R.Galovich
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A40
zbMATH DE Number: 1331478
zbMATH Keywords: enumeration
zbMATH Keywords: lattice paths
zbMATH Keywords: initial value problem
zbMATH Keywords: finite operator calculus
MaRDI profile type: Publication
cites work: Q4393357
cites work: Q4353153
cites work: On the foundations of combinatorial theory. VIII: Finite operator calculus
description: scientific article; zbMATH DE number 1331478