相关论文: The augmented external activity complex of a matro…

In this paper we establish a variation of the Splitter Theorem. Let $M$ and $N$ be simple 3-connected matroids. We say that $x\in E(M)$ is vertically $N$-contractible if $si(M/x)$ is a 3-connected matroid with an $N$-minor. Whittle (for…

We present a number of lower bounds for the h-vectors of k-CM, broken circuit and independence complexes. These lead to bounds on the coefficients of the characteristic and reliability polynomials of matroids. The main techniques are the…

Let $(h_0,h_1,\ldots,h_s)$ with $h_s\ne0$ be the $h$-vector of the broken circuit complex of a series-parallel network $M$. Let $G$ be a graph whose cycle matroid is $M$. We give a formula for the difference $h_{s-1}-h_1$ in terms of an ear…

Unit interval and interval complexes are higher-dimensional generalizations of unit interval and interval graphs, respectively. We show that strongly connected unit interval complexes are shellable with shellings induced by their unit…

A graph $G$ is said to be chordal if it has no induced cycles of length four or more. In a recent preprint Culbertson, Guralnik, and Stiller give a new characterization of chordal graphs in terms of sequences of what they call…

The active bijection for oriented matroids (and real hyperplane arrangements, and graphs, as particular cases) is introduced and investigated by the authors in a series of papers. Given any oriented matroid defined on a linearly ordered…

Adding elements to matroids can be fraught with difficulty. In the V\'amos matroid $V_8$, there are four independent sets $X_1,X_2, X_3,$ and $X_4$ such that $(X_1 \cup X_2,X_3 \cup X_4)$ is a $3$-separation while exactly three of the local…

We introduce and study strongly vertex dismissible, vertex dismissible, and scalable simplicial complexes as non-pure extensions of vertex decomposability and shellability. Strong vertex dismissibility is defined recursively by relaxing the…

This paper introduces a new and simple statistic on noncrossing partitions that expresses each coordinate of the toric $h$-vector of a cubical complex, written in the basis of the Adin $h$-vector entries, as the total weight of all…

We study the excitable Greenberg-Hastings cellular automaton model on scale-free networks. We obtained analytical expressions for no external stimulus and the uncoupled case. It is found that the curves, the average activity $F$ versus the…

Activity and renewability are distinctive features of living matter, and constitute a new class of materials that we term renewable active matter. A striking example is the cell cytoskeleton, where myosin filaments bind to the actin…

We first give two new proofs of an old result that the reduced Euler characteristic of a matroid complex is equal to the M\"obius number of the lattice of cycles of the matroid up to the sign. The purpose has been to find a model to…

We partition in classes the set of matroids of fixed dimension on a fixed vertex set. In each class we identify two special matroids, respectively with minimal and maximal h-vector in that class. Such extremal matroids also satisfy a…

A subcomplex $\mathcal{X}$ of a cell complex $\mathcal{C}$ is called \emph{rigid} with respect to another cell complex $\mathcal{C}'$ if every injective simplicial map $\lambda:\mathcal{X} \rightarrow \mathcal{C}'$ has a unique extension to…

Matroids over skew tracts provide an algebraic framework simultaneously generalizing the notions of linear subspaces, matroids, oriented matroids, phased matroids, and some other ``matroids with extra structure". A single-element extension…

The production of mechanical stresses in living organisms largely relies on localized, force-generating active units embedded in filamentous matrices. Numerical simulations of discrete fiber networks with fixed boundaries have shown that…

We investigate when the independence complex of $G[H]$, the lexicographical product of two graphs $G$ and $H$, is either vertex decomposable or shellable. As an application, we construct an infinite family of graphs with the property that…

We give a new proof of the fact that the complement of the complexification of a real hyperplane arrangement is homotopy equivalent to the Salvetti complex of the associated oriented matroid. Our proof involves no choices, is relatively…

Las Vergnas introduced several lattice structures on the bases of an ordered matroid M by using their external and internal activities. He also noted that when computing the Moebius function of these lattices, it was often zero, although he…

We extend the definition of chordal from graphs to clutters. The resulting family generalizes both chordal graphs and matroids, and obeys many of the same algebraic and geometric properties. Specifically, the independence complex of a…