论文标题
矩阵马尔可夫复杂性的渐近行为
Asymptotic behavior of Markov complexity of matrices
论文作者
论文摘要
对于任何整数矩阵$ a $ a $都可以将由图和另一个整数矩阵$ a_b $组成的矩阵结构关联。该图的连接组件称为花束。我们证明，花束对$ r $ - 矩阵的劳伦斯举重表现良好，我们用它来证明Markov和Graver的复杂性为$ M \ times n $等级$ d $的矩阵可能是任意的，对于$ n \ geQ 4 $和$ d \ d \ d \ leq n-2 $。相比之下，我们表明它们以$ n $和最大的绝对值$ a $ a $ a $ a $的最大限制。
To any integer matrix $A$ one can associate a matroid structure consisting of a graph and another integer matrix $A_B$. The connected components of this graph are called bouquets. We prove that bouquets behave well with respect to the $r$--th Lawrence liftings of matrices and we use it to prove that the Markov and Graver complexities of $m\times n$ matrices of rank $d$ may be arbitrarily large for $n\geq 4$ and $d\leq n-2$. In contrast, we show they are bounded in terms of $n$ and the largest absolute value $a$ of any entry of $A$.
