 
Summary: Solution Spaces of HSystems and the OreSato Theorem
S. A. Abramov
Russian Academy of Sciences
Dorodnicyn Computing Centre
Vavilova 40, 119991, Moscow GSP1, Russia
sabramov@ccas.ru
M. Petkovsek
Faculty of Mathematics and Physics
University of Ljubljana,
Jadranska 19, SI1000 Ljubljana, Slovenia
marko.petkovsek@fmf.unilj.si
Abstract
An Hsystem is a system of firstorder linear homogeneous difference equations for a single unknown
function T, with coefficients which are polynomials with complex coefficients. We consider solutions of
Hsystems which are of the form T : dom(T) C where either dom(T) = Zd
, or dom(T) = Zd
\ S and
S is the set of integer singularities of the system. It is shown that any natural number is the dimension
of the solution space of some Hsystem, and that in the case d 2 there are Hsystems whose solution
space is infinitedimensional. The relationships between dimensions of solution spaces in the two cases
