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ЖУРНАЛЫ // Algebra and Discrete Mathematics // Архив

Algebra Discrete Math., 2019, том 27, выпуск 2, страницы 155–164 (Mi adm700)

RESEARCH ARTICLE

A family of doubly stochastic matrices involving Chebyshev polynomials

Tanbir Ahmed, José M. R. Caballero

LaCIM, UQÁM, Montréal, Canada

Аннотация: 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).

Ключевые слова: doubly stochastic matrices, Chebyshev polynomials.

MSC: 05D10

Поступила в редакцию: 25.10.2017
Исправленный вариант: 29.12.2017

Язык публикации: английский



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