Number of inaccessible states in finite dynamic systems of binary vectors associated with palms orientations | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2015. № 3(29).

Finite dynamic systems of binary vectors associated with palms orientations are considered. A palm is a tree which is a union of paths having a common end vertex and all these paths, except perhaps one, have the length 1. States of a dynamic system (P _s+ _c, y), s > 0, с > 1, are all possible orientations of a palm with trunk length s and leafs number c, and evolutionary function y transforms the given palm orientations by reversing all arcs that enter into sinks. The following formula for the number of inaccessible states in the considered dynamic systems is proved: [(s-x)/4] os-x- s-x-3i. 2 + -2 -2 + Q(-1)-2Q(1)+Q(3), where Q(x) = £ (-1) -2 -С* i=1 As a corollary, the number of accessible states equals 2 + 2 3 - Q(-1) +2Q(1) - Q(3). The corresponding statistical tables for systems with different parameters s and с are given.