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Symbolic solutions of some linear recurrences

Authors
Journal
Journal of Statistical Planning and Inference
0378-3758
Publisher
Elsevier
Publication Date
Volume
142
Issue
2
Identifiers
DOI: 10.1016/j.jspi.2011.07.022
Keywords
  • Linear Recurrences
  • Sheffer Sequences
  • Classical Umbral Calculus
  • Dyck Paths
Disciplines
  • Mathematics

Abstract

Abstract A symbolic method for solving linear recurrences of combinatorial and statistical interest is introduced. This method essentially relies on a representation of polynomial sequences as moments of a symbol that looks as the framework of a random variable with no reference to any probability space. We give several examples of applications and state an explicit form for the class of linear recurrences involving Sheffer sequences satisfying a special initial condition. The results here presented can be easily implemented in a symbolic software.

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