On number of inaccessible states in finite dynamic systems of binary vectors associated with palms orientations

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, c > 1, are all possible orientations of a palm with trunk length s and leafs number c, and evolutionary function transforms a given palm orientation by reversing all arcs that enter into sinks. This dynamic system is isomorphic to finite dynamic system (B + , y), s > 0, c > 1, where states of this system are all possible binary vectors of dimension s + c. Let v = v ₁... v _S.v _S+1... v _s+ _c е B + , then y(v) = v' where v' is obtained by simultaneous application of the following rules: 1) if v ₁ = 0, then v' = 1; 2) if v _i = 1 and v _i+1 = 0 for some i where 0 < i < s, then vj = 0 and vj ₊₁ = 1; 3) if vi =1 for some i where s < i ^ s + c, then vj = 0; 4) if v _s = 1 and vi = 0 for all i where s < i ^ s + c, then vS = 0 and vj = 1 for all i, s < i ^ s + c; 5) there are no other differences between v and y(v). A formula for counting the number of inaccessible states in the considered dynamic systems is proposed. The table with the number of inaccessible states in systems (B + , y) for 1 < c < 9 is given.

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