The Cyclic Groups and the Semigroups via MacWilliams and Chebyshev Matrices

Abstract

In this paper, we consider the multiplicative orders of the MacWilliams matrix of order N(M N ) i j and the Chebyshev matrix of order N(D N ) i j according to modulo m for N ≥ 1. Consequently, we obtained the rules for the orders of the cyclic groups and semigroups generated by reducing the MacWilliams and Chebyshev matrices modulo m and the deteminats of these matrices.

Some aspects of Neyman triangles and Delannoy arrays

“…The research on the conformity of a single term, ; see for example, [5,6,7,8,10,12,14,16,17,18,29,30]. We now extend the concept to the complex-type Delannoy numbers.…”

Arithmetic Triangle

“…Several papers have been recently produced concerning Stirling numbers and cyclic groups, for instance (Broder, 1984) and (Deveci & Akuzum, 2014); or Pascal matrices (Deveci & Karaduman, 2012) and (Hiller, 2016). But they don't seem especially relevant to this article, which essentially deals with basic stuff.…”

The Cyclic Groups via Bezout Matrices

“…In (Deveci & Akuzum, 2014;Deveci & Karaduman, 2012;Deveci & Karaduman, in press;Deveci, et al, in press;Lü & Wang, 2007;Ozkan, 2014;, the authors obtained the cyclic groups via some special matrices. In this paper, we define the Bezout matrices by the aid of the characteristic polynomials of the k-step Fibonacci, the generalized order-k Pell and the generalized order-k Jacobsthal sequences.…”