论文标题
二进制矩阵的决定因素达到的每个积分值最高$ω（2^n/n）$
Determinants of binary matrices achieve every integral value up to $Ω(2^n/n)$
论文作者
论文摘要
这项工作表明，最小的自然数$ d_n $不是某些$ n \ times n $ binary矩阵的决定因素，至少是$ c \，2^n/n $ for $ c = 1/201 $。同样的数量自然下降界限不同的整数$ d_n $的数量，这些数量可以写为某些$ n \ times n $二进制矩阵的决定因素。此渐近地改善了$ d_n =ω（1.618^n）$的先前结果，并稍微改善了特定$ g（n）=ω（n^2）$函数的$ d_n \ ge 2^n/g（n）$的先前结果。
This work shows that the smallest natural number $d_n$ that is not the determinant of some $n\times n$ binary matrix is at least $c\,2^n/n$ for $c=1/201$. That same quantity naturally lower bounds the number of distinct integers $D_n$ which can be written as the determinant of some $n\times n$ binary matrix. This asymptotically improves the previous result of $d_n=Ω(1.618^n)$ and slightly improves the previous result of $D_n\ge 2^n/g(n)$ for a particular $g(n)=ω(n^2)$ function.
