Journal of Physical Studies 15(2), Article 2001 [16 pages] (2011)


A. Olemskoi{1,2}, S. Borysov2, I. Shuda2

1Institute of Applied Physics, Nat. Acad. Sci. of Ukraine,
58, Petropavlovskaya St., 40030, Sumy, Ukraine
2Sumy State University, 2, Rimskii-Korsakov St., 40007, Sumy, Ukraine

We consider both analytically and numerically the creation conditions of diverse hierarchical trees. A connection between the probabilities to create hierarchical levels and the probability to associate these levels into a united structure are 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 and free-scale trees are determined numerically. We find a general expression for the creation probability of an arbitrary tree and calculate the sum of terms of deformed geometrical progression that results from the consideration of the degenerate tree.

PACS number(s): 02.50.-r, 89.75.-k, 89.75.Fb