Minimal universal denominators for systems of linear recurrences. Issue 10 (2nd October 2016) - Mu, Yan-Ping
Abstract : Abramov's algorithm provides universal denominators for rational solutions to the system of linear recurrences of the form Y ( x + 1 ) = A ( x ) Y ( x ) + G ( x ) . We show that in general Abramov's estimation is optimal. Meanwhile, we show that better estimations can be obtained when A ( x ) is a triangular matrix and when A ( x ) is a constant matrix up to a scalar factor.