7 papers · 1 filter
Füredi's Conjecture and a Sharp Strengthening
Zihao Huang, Suijie Wang
We prove a strengthening of Füredi's conjecture on strong Bollobás -systems. For nonnegative integers and , a family of pairs of finite sets satisfyin…
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…
Covering Hypercube
Zihao Huang, Miao Wang, Suijie Wang
The Alon--Füredi theorem determines the minimum number of hyperplanes needed to cover every nonzero vertex of the Boolean cube while avoiding the origin. We study hyperplane coveri…
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…
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…