Algebra and Discrete Mathematics. - № 2 (27). - 2019http://hdl.handle.net/123456789/43792024-03-29T08:02:17Z2024-03-29T08:02:17ZA family of doubly stochastic matrices involving chebyshev polynomialsAhmed, T.Caballero, J.M.R.http://hdl.handle.net/123456789/43892020-01-08T15:04:52Z2019-01-01T00:00:00ZA family of doubly stochastic matrices involving chebyshev polynomials
Ahmed, T.; Caballero, J.M.R.
A doubly stochastic matrix is a square matrix
A = (aij ) of non-negative real numbers such that P
i
aij =
P
j
aij = 1.
The Chebyshev polynomial of the first kind is defined by the recur-
rence relation T0(x) = 1, T1(x) = x, and
Tn+1(x) = 2xTn(x) − Tn−1(x).
In this paper, we show a 2
k × 2
k
(for each integer k > 1) doubly
stochastic matrix whose characteristic polynomial is x
2 − 1 times
a product of irreducible Chebyshev polynomials of the first kind
(upto rescaling by rational numbers).
Ahmed T. A family of doubly stochastic matrices involving Chebyshev polynomials / J.M.R.Caballero // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 2. - Рp.155-164
2019-01-01T00:00:00ZAutomorphism groups of superextensions of finite monogenic semigroupsBanakh, T.Gavrylkiv, V.http://hdl.handle.net/123456789/43882020-01-08T15:04:55Z2019-01-01T00:00:00ZAutomorphism groups of superextensions of finite monogenic semigroups
Banakh, T.; Gavrylkiv, V.
A family L of subsets of a set X is called linked
if A ∩ B 6= ∅ for any A, B ∈ L. A linked family M of subsets of
X is maximal linked if M coincides with each linked family L on
X that contains M. The superextension λ(X) of X consists of all
maximal linked families on X. Any associative binary operation
∗ : X × X → X can be extended to an associative binary operation
∗ : λ(X) × λ(X) → λ(X). In the paper we study automorphisms
of the superextensions of finite monogenic semigroups and charac-
teristic ideals in such semigroups. In particular, we describe the
automorphism groups of the superextensions of finite monogenic
semigroups of cardinality 6 5.
Banakh T. Automorphism groups of superextensions of finite monogenic semigroups / T.Banakh , V. Gavrylkiv // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 2. - Рp.165-190
2019-01-01T00:00:00ZOn cospectral signed digraphsBhat, M. A.Naikoo, T. A.Pirzada, S.http://hdl.handle.net/123456789/43872020-01-08T15:04:54Z2019-01-01T00:00:00ZOn cospectral signed digraphs
Bhat, M. A.; Naikoo, T. A.; Pirzada, S.
The set of distinct eigenvalues of a signed digraph S together with their respective multiplicities is called its spectrum. Two signed digraphs of same order are said to be cospectral if they have the same spectrum. In this paper, we show the existence of integral, real and Gaussian cospectral signed digraphs.We give a spectral characterization of normal signed digraphs and use it to construct cospectral normal signed digraphs.
Bhat M.A. On cospectral signed digraphs / M.A.Bhat , T . A.Naikoo , S.Pirzada // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 2. - Рp.191-201
2019-01-01T00:00:00ZThe classification of serial posets with the non-negative quadratic tits form being principalBondarenko, V.Styopochkina, M.http://hdl.handle.net/123456789/43862020-01-08T15:04:52Z2019-01-01T00:00:00ZThe classification of serial posets with the non-negative quadratic tits form being principal
Bondarenko, V.; Styopochkina, M.
Using (introduced by the first author) the method
of (min, max)-equivalence, we classify all serial principal posets, i.e.
the posets S satisfying the following conditions: (1) the quadratic
Tits form qS(z) : Z
|S|+1 → Z of S is non-negative; (2) Ker qS(z) :=
{t| qS(t) = 0} is an infinite cyclic group (equivalently, the corank
of the symmetric matrix of qS(z) is equal to 1); (3) for any m ∈ N,
there is a poset S(m) ⊃ S such that S(m) satisfies (1), (2) and
|S(m) \ S| = m.
Bondarenko V. The classification of serial posets with the non-negative quadratic tits form being principal / V. Bondarenko , M .Styopochkina // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 2. - Рp.202 -211
2019-01-01T00:00:00Z