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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}$. 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