{"paper":{"title":"Isoperimetric Sequences for Infinite Complete Binary Trees, Meta-Fibonacci Sequences and Signed Almost Binary Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anita Das, Frank Ruskey, L. Sunil Chandran","submitted_at":"2012-10-01T13:57:34Z","abstract_excerpt":"In this paper we demonstrate connections between three seemingly unrelated concepts.\n  (1) The discrete isoperimetric problem in the infinite binary tree with all the leaves at the same level, $ {\\mathcal T}_{\\infty}$:\n  The $n$-th edge isoperimetric number $\\delta(n)$ is defined to be $\\min_{|S|=n, S \\subset V({\\mathcal T}_{\\infty})} |(S,\\bar{S})|$,\nwhere $(S,\\bar{S})$ is the set of edges in the cut defined by $S$.\n  (2) Signed almost binary partitions: This is the special case of the coin-changing problem where the coins are drawn from the set\n  ${\\pm (2^d - 1): $d$ is a positive integer}$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0405","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"}