{"paper":{"title":"Greedy and lazy representations in negative base systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Edita Pelantov\\'a, Tom\\'a\\v{s} Hejda, Zuzana Mas\\'akov\\'a","submitted_at":"2011-10-28T13:23:31Z","abstract_excerpt":"We consider positional numeration systems with negative real base $-\\beta$, where $\\beta>1$, 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 $\\beta^2$ and a non-integer alphabet. This enables us to characterize digit sequences admissible as greedy and lazy $(-\\beta)$-representation. Such a characterization allows "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6327","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}