http://hdl.handle.net/123456789/4379 Wed, 15 Apr 2026 21:39:05 GMT 2026-04-15T21:39:05Z http://hdl.handle.net/123456789/4389 A 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 Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/123456789/4389 2019-01-01T00:00:00Z http://hdl.handle.net/123456789/4388 Automorphism 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 Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/123456789/4388 2019-01-01T00:00:00Z http://hdl.handle.net/123456789/4387 On 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 Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/123456789/4387 2019-01-01T00:00:00Z http://hdl.handle.net/123456789/4386 The 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 Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/123456789/4386 2019-01-01T00:00:00Z