Negative Pisot Numbers from Alternating-Sign Characteristic Polynomials

Abstract
We study a family of characteristic polynomials with alternating signs for degrees
n = 2 to 21. For every odd degree n ≥ 3 the polynomial has a unique negative real root
of modulus greater than one, while all other roots lie strictly inside the unit circle. These
numbers are therefore negative Pisot numbers. The moduli increase with n and converge
to 2 from below. This explicit infinite family complements earlier results of Hare and
Mossinghoff (2014) on negative Pisot numbers in the interval (−(1 +
√
5)/2,−1).