7 papers · 1 filter
Nice Partitions, Supersolvability, and Freeness in Deformations of Graphic Arrangements
Weikang Liang, Suijie Wang, Yue Zhou
We study affine deformations of graphic arrangements and their cones. Here is a simple graph, is a family of fi…
Freeness of Arrangements with Regular Underlying Matroids
Weikang Liang, Suijie Wang
We classify freeness for finite central arrangements whose underlying matroids are regular. Let be such an arrangement over an arbitrary field, and put $M=M(\mathcal A…
Level of Faces for Exponential Sequence of Arrangements
Yanru Chen, Houshan Fu, Weikang Liang +1
In this paper, we introduce the bivariate exponential generating function for the number of level- faces of an exponential sequence of arrangements (ESA), and establi…
Several New Generalizations of LYM Inequality
Zihao Huang, Weikang Liang, Yujiao Ma +1
The LYM inequality is a fundamental result concerning the sizes of subsets in a Sperner family. Subsequent studies on the LYM inequality have been generalized to families of -de…
A decomposition of Grassmannian associated with a hyperplane arrangement
Houshan Fu, Weikang Liang, Suijie Wang
The Grassmannian, which is the manifold of all -dimensional subspaces in the Euclidean space , was decomposed through three equivalent methods connecting combinato…
Characterizing Nice Partition of Graphical Arrangements
Weikang Liang, Suijie Wang, Chengdong Zhao
The successive works of Terao as well as Stanley revealed that, for graphical arrangements, supersolvability and the existence of nice partitions are equivalent properties, both ch…
-Adjoint of Hyperplane Arrangements
Weikang Liang, Suijie Wang, Chengdong Zhao
In this paper, we introduce the -adjoint of a given hyperplane arrangement associated with rank- elements in the intersection lattice , which ge…