%0 Journal Article
%T Ambiguity in the m-bonacci numeration system
%A Petra Koc¨¢bov¨¢
%A Zuzana Mas¨¢kov¨¢
%A Edita Pelantov¨¢
%J Discrete Mathematics & Theoretical Computer Science
%D 2007
%I Discrete Mathematics & Theoretical Computer Science
%X We study the properties of the function R (m) (n) defined as the number of representations of an integer n as a sum of distinct m-Bonacci numbers F (m) k, given by F i (m) =2 i-1, for i¡Ê { 1, 2, ¡­, m}, F k+m (m) =F k+m-1 (m) +F k+m-2 (m) +   + F k (m), for k ¡Ý 1. We give a matrix formula for calculating R (m) (n) from the greedy expansion of n. We determine the maximum of R (m) (n) for n with greedy expansion of fixed length k, i.e. for F (m) k ¡Ü n
%U http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/660