Timashev, Aleksandr N.
Published in
Discrete Mathematics and Applications

Several classes of distributions of power series type with finite and infinite radii of convergence are considered. For such distributions local limit theorems are obtained as the parameter of distribution tends to the right end of the interval of convergence. For the case when the convergence radius equals to 1, we prove an integral limit theorem ...

Taletskii, Dmitriy S. Malyshev, Dmitriy S.
Published in
Discrete Mathematics and Applications

For any n, in the set of n-vertex trees such that any two leaves have no common adjacent vertex, we describe the trees with the smallest number of maximal independent sets.

Chudnov, Alexander M.
Published in
Discrete Mathematics and Applications

Sapozhenko, Aleksandr A. Sargsyan, Vahe G.
Published in
Discrete Mathematics and Applications

A family (A1, …, Ak) of subsets of a group G is called k-solution-free family if the equation x1 + … + xk = 0 has no solution in (A1, …, Ak) such that x1 ∈ A1, …, xk ∈ Ak. We find the asymptotic behavior for the logarithm of the number of k-solution-free families in Abelian groups.

Kuz’min, Leonid V.
Published in
Discrete Mathematics and Applications

The paper is concerned with systems of incidence involving a space of points X and lines consisting of q points each. A free space X is defined. For a space X an analogue of the Burnside problem (solved in the negative) and an analogue of the weakened Burnside problem are formulated. In the case q = 3 the positive answer to the analogue of the weak...

Yakymiv, Arsen L.
Published in
Discrete Mathematics and Applications

Let B(x) be a multiple power series with nonnegative coefficients which is convergent for all x ∈ (0, 1)n and diverges at the point 1 = (1, …, 1). Random vectors (r.v.)ξx such that ξx has distribution of the power series B(x) type is studied. The integral limit theorem for r.v. ξx as x ↑ 1 is proved under the assumption that B(x) is regularly varyi...

Malyshev, Fedor M.
Published in
Discrete Mathematics and Applications

We give an elementary proof that by multiplication on left and right by affine permutations A, B ∈ AGL(3, 2) each permutation π : GF(2)3 → GF(2)3 may be reduced to one of the 4 permutations for which the 3 × 3-matrices consisting of the coefficients of quadratic terms of coordinate functions have as an invariant the rank, which is either 3, or 2, o...

Ivanov, Ilya E.
Published in
Discrete Mathematics and Applications

Finite automata transform periodic sequences into periodic ones. The period of the output sequence is bounded from above by a linear function of input period. It is known that pushdown automata also preserve the set of periodic sequences. We prove that the output period for one-counter pushdown automata is bounded from above by a quadratic function...

Orlov, Oleg P.
Published in
Discrete Mathematics and Applications

For sets of iid random points having a uniform (in a definite sense) distribution on the arbitrary metric space a maximal distance to the nearest neighbour is considered. By means of the Chen–Stein method new limit theorems for this random variable is proved. For random uniform samples from the set of binary cube vertices analogous results are obta...

Polin, Sergey V.
Published in
Discrete Mathematics and Applications

The paper is devoted to the study of equations with the left-hand side having the form of a composition of operations which belong to given sets S1, …, Sn, … of quasigroup operations. Elementary transformations are described which allow reducing systems of this kind to the form where all equations except one do not depend essentially on the variabl...