GREEDY AND LAZY REPRESENTATIONS IN NEGATIVE BASE SYSTEMS

作者：Hejda Tomas^*; Masakova Zuzana; Pelantova Edita

来源：Kybernetika, 2013, 49(2): 258-279.

• numeration systems
• lazy representation
• greedy representation
• negative base
• unique representation

We consider positional numeration systems with negative real base -beta, where beta%26gt; 1, and study the extremal representations in these systems, called here the greedy and lazy representations. We give algorithms for determination of minimal and maximal (-beta)-representation with respect to the alternate order. We also show that both extremal representations can be obtained as representations in the positive base beta(2) with a non-integer alphabet. This enables us to characterize digit sequences admissible as greedy and lazy (-beta)-representation. Such a characterization allows us to study the set of uniquely representable numbers. In the case that is the golden ratio and the Tribonacci constant, we give the characterization of digit sequences admissible as greedy and lazy (-beta)-representation using a set of forbidden strings.

• 出版日期2013