Asymptotic behavior of two-terminal series-parallel networks

1997/07/02 by O. Golinelli, Golinelli, O.
Computer Science · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Cellular Automata and Applications #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/9707023

9 pages, revtex, 18 eps figures (uses epsf)

arxiv created 1997/07/02 · openalex publication_date 1997/07/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper discusses the enumeration of two-terminal series-parallel networks, i.e. the number of electrical networks built with n identical elements connected in series or parallel with two-terminal nodes. They frequently occur in applied probability theory as a model for real networks. The number of networks grows asymptotically like Rⁿ/n^alpha, as for some models of statistical physics like self-avoiding walks, lattice animals, meanders, etc. By using a exact recurrence relation, the entropy is numerically estimated at R = 3.5608393095389433(1), and we show that the sub-leading universal exponent alpha is 3/2.

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