论文标题
惠特尼的部分道林格尔特。
Whitney Numbers of Partial Dowling Lattices
论文作者
论文摘要
Dowling晶格$ q_n（\ Mathfrak {g}）$，$ \ Mathfrak {g} $有限组，概括了所有向量在一个字段上生成的几何晶格，其中最多有两个非零组件。抽象地，它是有限矩形分类的基本对象。从建设性上讲，它是某个增益图的帧矩阵，称为$ \ mathfrak {g} {\ cdot} k_n^{（v）} $。其第一类的惠特尼人数进入了几个重要的公式。 Ravagnani建议并部分证明了这些数字的$ q_n（\ Mathfrak {g}）$，更高的概括是$ | \ Mathfrak {g} | $的多项式函数。我们给出了$ q_n（\ mathfrak {g}）$的简单证明及其对更广泛的增益图和偏置图的概括，我们确定多项式的程度和系数。
The Dowling lattice $Q_n(\mathfrak{G})$, $\mathfrak{G}$ a finite group, generalizes the geometric lattice generated by all vectors, over a field, with at most two nonzero components. Abstractly, it is a fundamental object in the classification of finite matroids. Constructively, it is the frame matroid of a certain gain graph known as $\mathfrak{G}{\cdot}K_n^{(V)}$. Its Whitney numbers of the first kind enter into several important formulas. Ravagnani suggested and partially proved that these numbers of $Q_n(\mathfrak{G})$ and higher-weight generalizations are polynomial functions of $|\mathfrak{G}|$. We give a simple proof for $Q_n(\mathfrak{G})$ and its generalization to a wider class of gain graphs and biased graphs, and we determine the degrees and coefficients of the polynomials.
