Characteristic polynomials of some min and max matrices

Abstract

In this paper, we investigate Min matrices [Formula: see text] and Max matrices [Formula: see text] whose entries are [Formula: see text] and [Formula: see text], respectively, where [Formula: see text] and [Formula: see text]. By utilizing combinatorial identities, we derive the characteristic polynomials of M and U. Additionally, relationship between generalized Fibonacci numbers and the characteristic polynomials of these matrices is established. Finally, some examples are given to illustrate our results.

Keywords

• Min and Max matrices
• binomial coefficient
• characteristic polynomial
• principal minor
• generalized Fibonacci number