Condensed Matter Physics, 2011, vol. 14, No. 1, 14001: 1-6 (Rapid Communications)
DOI:10.5488/CMP.14.14001          arXiv:1106.3578

Title: Analytical and numerical studies of creation probabilities of hierarchical trees
  A.I. Olemskoi (Institute of Applied Physics, Nat. Acad. Sci. of Ukraine, 58 Petropavlivs'ka Str., 40030 Sumy, Ukraine) ,
  S.S. Borysov (Sumy State University, 2 Rimskii-Korsakov Str., 40007 Sumy, Ukraine) ,
  I.A. Shuda (Sumy State University, 2 Rimskii-Korsakov Str., 40007 Sumy, Ukraine)

We consider the creation conditions of diverse hierarchical trees both analytically and numerically. A connection between the probabilities to create hierarchical levels and the probability to associate these levels into a united structure is studied. We argue that a consistent probabilistic picture requires the use of deformed algebra. Our consideration is based on the study of the main types of hierarchical trees, among which both regular and degenerate ones are studied analytically, while the creation probabilities of Fibonacci, scale-free and arbitrary trees are determined numerically.

Key words: probability, hierarchical tree, deformation
PACS: 02.50.-r, 89.75.-k, 89.75.Fb
Comments: Figs. 3, Refs. 14

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