6 papers · 1 filter
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…