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STRUCTURE OF THE PATH LENGTH SET IN ASYMMETRIC TREES

CHLOE EPSTEIN

Department of Mathematics, Ithaca College, 402A Williams Hall, Ithaca, NY 14850, USA

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WILLIAM SENDEWICZ

Department of Mathematics, Ithaca College, 402A Williams Hall, Ithaca, NY 14850, USA

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, and

DAVID BROWN

Department of Mathematics, Ithaca College, 402A Williams Hall, Ithaca, NY 14850, USA

Corresponding author.

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https://doi.org/10.1142/S0218348X05002969Cited by:1 (Source: Crossref)

Abstract

We characterize the path length set of asymmetric binary fractal trees in terms of the scaling ratios, r and ℓ. We show that if r + ℓ < 1, then the path length set is a Cantor set, and if r + ℓ ≥ 1, then the path length set is an interval.

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