Maximum Absolute Determinants of Upper Hessenberg Bohemian Matrices

Abstract: A matrix is called Bohemian if its entries are sampled from a finite set of integers. We determine the maximum absolute determinant of upper Hessenberg Bohemian Matrices for which the subdiagonal entries are fixed to be $1$ and upper triangular entries are sampled from ${0,1,\cdots,n}$, extending previous results for $n=1$ and $n=2$ and proving a recent conjecture of Fasi & Negri Porzio [8]. Furthermore, we generalize the problem to non-integer-valued entries.