Geodesic
A family of doubly stochastic matrices involving Chebyshev polynomials
Algebra and discrete mathematics, Tome 27 (2019) no. 2, pp. 155-164

Voir la notice de l'article provenant de la source Math-Net.Ru

A doubly stochastic matrix is a square matrix $A=(a_{ij})$ of non-negative real numbers such that $\sum_{i}a_{ij}=\sum_{j}a_{ij}=1$. The Chebyshev polynomial of the first kind is defined by the recurrence relation $T_0(x)=1$, $T_1(x)=x$, and $$ T_{n+1}(x)=2xT_n(x)-T_{n-1}(x). $$ In this paper, we show a $2^k\times 2^k$ (for each integer $k\geq 1$) doubly stochastic matrix whose characteristic polynomial is $x^2-1$ times a product of irreducible Chebyshev polynomials of the first kind (up to rescaling by rational numbers).
Keywords: doubly stochastic matrices, Chebyshev polynomials. 
@article{ADM_2019_27_2_a1,
     author = {Tanbir Ahmed and Jos\'e M. R. Caballero},
     title = {A family of doubly stochastic matrices involving {Chebyshev} polynomials},
     journal = {Algebra and discrete mathematics},
     pages = {155--164},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2019_27_2_a1/}
}
TY  - JOUR
AU  - Tanbir Ahmed
AU  - José M. R. Caballero
TI  - A family of doubly stochastic matrices involving Chebyshev polynomials
JO  - Algebra and discrete mathematics
PY  - 2019
SP  - 155
EP  - 164
VL  - 27
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2019_27_2_a1/
LA  - en
ID  - ADM_2019_27_2_a1
ER  - 
%0 Journal Article
%A Tanbir Ahmed
%A José M. R. Caballero
%T A family of doubly stochastic matrices involving Chebyshev polynomials
%J Algebra and discrete mathematics
%D 2019
%P 155-164
%V 27
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2019_27_2_a1/
%G en
%F ADM_2019_27_2_a1
Tanbir Ahmed; José M. R. Caballero. A family of doubly stochastic matrices involving Chebyshev polynomials. Algebra and discrete mathematics, Tome 27 (2019) no. 2, pp. 155-164. http://geodesic.mathdoc.fr/item/ADM_2019_27_2_a1/