Negative Pisot Numbers from Alternating-Sign Characteristic Polynomials

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