# Maximum Absolute Determinants of Upper Hessenberg Bohemian Matrices

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,⋯,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.

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