A Representation Theorem for Holonomic Sequences Based on Counting Lattice Paths

Authors:
Tomer Kotek;Johann A. Makowsky
Affiliations:
(Partially supported by a grant of the Graduate School of the Technion-Israel Institute of Technology) Department of Computer Science, Technion-Israel Institute of Technology, 32000 Haifa, Israel, ...;(Correspd.) (Partially supported by a grant of the Fund for Promotion of Research of the Technion-Israel Institute of Technology and grant ISF 1392/07 of the Israel Science Foundation (2007-2011)) ...
Venue:
Fundamenta Informaticae - Lattice Path Combinatorics and Applications
Year:
2012

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Abstract

Using a theorem of N. Chomsky and M. Schützenberger one can characterize sequences of integers which satisfy linear recurrence relations with constant coefficients (C-finite sequences) as differences of two sequences counting words in regular languages. We prove an analog for P-recursive (holonomic) sequences in terms of counting certain lattice paths.