{"paper":{"title":"Left-Right Pairs and Complex Forests of Infinite Rooted Binary Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nina Zubrilina","submitted_at":"2018-10-10T03:15:17Z","abstract_excerpt":"Let $\\mathcal{D}_0:= \\{x + iy \\ \\vert x, y >0\\}$, and let $(L, R)$ be a pair of M\\\"{o}bius transformations corresponding to $\\mathrm{SL}_2(\\mathbb{N}_0)$ matrices such that $R(\\mathcal{D}_0)$ and $L(\\mathcal{D}_0)$ are disjoint. Given such a pair (called a left-right pair), we can construct a directed graph $\\mathcal{F}(L, R)$ with vertices $\\mathcal{D}_0$ and edges $\\{(z, R(z))\\}_{z \\in \\mathcal{D}_0} \\cup \\{(z, L(z))\\}_{z \\in \\mathcal{D}_0}$, which is a collection of infinite binary trees. We answer two questions of Nathanson by classifying all the pairs of elements of $\\mathrm{SL}_2(\\mathbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04349","kind":"arxiv","version":1},"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"}