Pascal \(k\)-eliminated functional matrix and its property
Let \(p\) be a prime, and let \(\mathbb{F}_p\) be the finite field with \(p\) elements. The authors mainly prove that if \(n\geq p+1\) and \(p|k\), then the minimal polynomial of the Pascal \(k\)-eliminated functional matrix \(P_{n,k}\) on \(\mathbb{F}_p\) is \((1-x)^p\), where \(n\) and \(k\) are positive integers. This is an affirmative answer to an open problem raised by \textit{M. Razpet} [Discrete Math. 135, No. 1-3, 377-379 (1994; Zbl 0819.05004)].
Pascal \(k\)-eliminated functional matrix
scientific article; zbMATH DE number 1443397