论文标题
特征曲霉的集合
Characteristic Sets of Matroids
论文作者
论文摘要
我们研究了可能的线性，代数和Frobenius羊群的特征组合。特别是，当代数特征集是有限的或cofinite时，我们将线性和代数特性集的可能组合分类。我们还表明，在素数中设置的代数特征的自然密度可能任意接近间隔$ [0,1] $中的任何实际数字。 Frobenius羊群实现可以从代数实现构建，但相反是不正确的。我们表明，即使对于frobenius羊群特征集的矩形，代数特征集也可能是任意的cofinite集合。此外，我们从特征0中的线性实现以及弗罗贝尼乌斯（Frobenius）群群实现双重基质中构建了Frobenius群蜂拥而至的实现。
We investigate possible linear, algebraic, and Frobenius flock characteristic sets of matroids. In particular, we classify possible combinations of linear and algebraic characteristic sets when the algebraic characteristic set is finite or cofinite. We also show that the natural density of an algebraic characteristic set in the set of primes may be arbitrarily close to any real number in the interval $[0,1]$. Frobenius flock realizations can be constructed from algebraic realizations, but the converse is not true. We show that the algebraic characteristic set may be an arbitrary cofinite set even for matroids whose Frobenius flock characteristic set is the set of all primes. In addition, we construct Frobenius flock realizations in all positive characteristics from linear realizations in characteristic 0, and also from Frobenius flock realizations of the dual matroid.
