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.

中文翻译：

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上 Hessenberg 波西米亚矩阵的最大绝对行列式

如果矩阵的条目是从一组有限整数中采样的，则该矩阵称为波西米亚矩阵。我们确定了上 Hessenberg 波西米亚矩阵的最大绝对行列式，其中对角线项固定为 $1$，上三角项从 $\{0,1,\cdots,n\}$ 中采样，扩展了 $n 的先前结果=1$ 和 $n=2$ 并证明了 Fasi & Negri Porzio [8] 最近的猜想。此外，我们将问题推广到非整数值条目。