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The peculiar (monic) polynomials, the zeros of which equal their coefficients

Calogero, F. ; Leyvraz, F.

Journal of nonlinear mathematical physics, 2017-01, Vol.24 (4), p.545-555 [Periódico revisado por pares]

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Título:
The peculiar (monic) polynomials, the zeros of which equal their coefficients
Autor: Calogero, F. ; Leyvraz, F.
Assuntos: Coefficients ; Polynomials ; Research Article ; Ulam polynomials ; zeros of polynomials
É parte de: Journal of nonlinear mathematical physics, 2017-01, Vol.24 (4), p.545-555
Descrição: We evaluate the number of complex monic polynomials, of arbitrary degree N, the zeros of which are equal to their coefficients. In the following, we call polynomials with this property peculiar polynomials. We further show that the problem of determining the peculiar polynomials of degree N simplifies when any of the coefficients is either 0 or 1. We proceed to estimate the numbers of peculiar polynomials of degree N having one coefficient zero, or one coefficient equal to one, or neither.
Editor: Dordrecht: Taylor & Francis
Idioma: Inglês

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