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. 
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     title = {A family of doubly stochastic matrices involving {Chebyshev} polynomials},
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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/

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