Proof of a conjecture of Lundow and Rosengren on the bimodality of -binomial coefficients

Lundow and Rosengren observed that the magnetization distributions of Ising model are remarkably well-fitted by the p , q -binomial distributions based on an assumption that the p , q -binomial distribution is unimodal or bimodal. In the present paper we show that this assumption holds for all positive numbers p and q.