15 papers
A counterexample to the circuit-cocircuit intersection conjecture
Houshan Fu
Oxley conjectured that a matroid with a circuit-cocircuit intersection of size has one of size . Using the standard polynomial representation of the classical extend…
Real-rootedness and ultra log-concavity of rank-two matroid Ehrhart -polynomials
Houshan Fu
We prove that the Ehrhart -polynomial of a rank-two matroid with exactly three parallel classes is real-rooted whenever its smallest parallel class has size at most three. Thi…
Log-Concavity of Conic Intrinsic Volumes
Houshan Fu, Suijie Wang
Let and be a closed convex cone with conic intrinsic volumes . We prove the long-standing log-concavity conjecture for this s…
Convolution-type Identity for Characteristic Polynomials of Geometric Semilattices
Yanru Chen, Houshan Fu, Ang Li +1
We establish a convolution formula for the characteristic polynomial of a finite geometric semilattice : \[ χ(M,st)=\sum_{X\in \underline{M}} s^{r-{\rm rk}_{\underline{M}}(X)}χ(…
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…
Characteristic quasi-polynomials of truncated arrangements
Ying Cao, Houshan Fu
Given an (affine) integral arrangement in , the reduction of modulo an arbitrary positive integer naturally yields an arrangement $\ma…
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…
Level of Regions for Deformed Braid Arrangements
Yanru Chen, Houshan Fu, Suijie Wang +1
This paper primarily investigates a specific type of deformation of the braid arrangement in , denoted by and defined in (1.2). Let…
Counting Flows of -compatible Graphs
Houshan Fu, Xiangyu Ren, Suijie Wang
Kochol introduced the assigning polynomial to count nowhere-zero -flows of a graph , where is a finite Abelian group and is a -assigning from…
Two Bijections on NBC Subsets
Houshan Fu, Baoren Peng, Suijie Wang +1
We establish two explicit bijections: from acyclic reorientations of an oriented matroid to no broken circuit (NBC) subsets of its underlying matroid, and from regions of a real hy…
Deformed Intersections of Half-spaces
Houshan Fu, Boxuan Li, Chunming Tang +1
This paper is devoted to the classification problems concerning extended deformations of convex polyhedra and real hyperplane arrangements in the following senses: combinatorial eq…
One-element Extensions of Hyperplane Arrangements
Hang Cai, Houshan Fu, Suijie Wang
We classify one-element extensions of a hyperplane arrangement by the induced adjoint arrangement. Based on the classification, several kinds of combinatorial invariants including…
Adjoints of Matroids
Houshan Fu, Chunming Tang, Suijie Wang
We show that an adjoint of a loopless matroid is connected if and only if it itself is connected. Our first goal is to study the adjoint of modular matroids. We prove that a modula…
Bijections on -Shi and -Catalan Arrangements
Houshan Fu, Suijie Wang, Weijin Zhu
Associated with the -Shi arrangement and -Catalan arrangement in , we introduce a cubic matrix for each region to establish two bijections in a uniform way. Firstl…
Truncated Homogeneous Symmetric Functions
Houshan Fu, Zhousheng Mei
Extending the elementary and complete homogeneous symmetric functions, we introduce the truncated homogeneous symmetric function $h_λ^{\dd}$ in $(\ref{THSF})$ for any integer parti…