Some remarks on permanental dominance conjecture

In this paper we provide an identity between the determinant and other generalized matrix functions, and give a criterion for positive semi-definite matrices to satisfy the permanental dominance conjecture. As a consequence, infinitely many classes of positive semi-definite matrices satisfying the conjecture (does not depend on groups or characters) are provided by generating from any positive semi-definite matrix having no zero in the first column. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.