Related papers: f-vectors of Simplicial Posets that are Balls
A simplicial cell ball is a simplicial poset whose geometric realization is homeomorphic to a ball. Recently, Samuel Kolins gave a series of necessary conditions and sufficient conditions on $h$-vectors of simplicial cell balls, and…
As is well known, h-vectors of simple (or simplicial) convex polytopes are characterized. In fact, those h-vectors must satisfy Dehn-Sommerville equations and some other inequalities. Simple convex polytopes determine Gorenstein* simplicial…
A relative simplicial complex is a collection of sets of the form $\Delta \setminus \Gamma$, where $\Gamma \subset \Delta$ are simplicial complexes. Relative complexes played key roles in recent advances in algebraic, geometric, and…
In this paper, we study face vectors of simplicial posets that are the face posets of cell decompositions of topological manifolds without boundary. We characterize all possible face vectors of simplicial posets whose geometric realizations…
The family of Buchsbaum simplicial posets generalizes the family of simplicial cell manifolds. The $h'$-vector of a simplicial complex or simplicial poset encodes the combinatorial and topological data of its face numbers and the reduced…
In this paper, we characterize all possible h-vectors of 2-dimensional Buchsbaum simplicial complexes.
We study Stanley's long-standing conjecture that the h-vectors of matroid simplicial complexes are pure O-sequences. Our method consists of a new and more abstract approach, which shifts the focus from working on constructing suitable…
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…
This thesis focuses on algebraic shifting and its applications to f-vector theory of simplicial complexes and more general graded posets. In particular, several approaches and partial results concerning the g-conjecture for simplicial…
We prove that if a pure simplicial complex of dimension d with n facets has the least possible number of (d-1)-dimensional faces among all complexes with n faces of dimension d, then it is vertex decomposable. This answers a question of J.…
We describe two methods for showing that a vector can not be the f-vector of a homology d-ball. As a consequence, we disprove a conjectured characterization of the f-vectors of balls of dimension five and higher due to Billera and Lee. We…
Given an infinite field $\mathbb{k}$ and a simplicial complex $\Delta$, a common theme in studying the $f$- and $h$-vectors of $\Delta$ has been the consideration of the Hilbert series of the Stanley--Reisner ring $\mathbb{k}[\Delta]$…
We give two proofs that the $h$-vector of any paving matroid is a pure O-sequence, thus answering in the affirmative a conjecture made by R. Stanley, for this particular class of matroids. We also investigate the problem of obtaining good…
A well-known conjecture of McMullen, proved by Billera, Lee and Stanley, describes the face numbers of simple polytopes. The necessary and sufficient condition is that the toric g-vector of the polytope is an M-vector, that is, the vector…
We consider geometric and computational measures of complexity for sets of integer vectors, asking for a qualitative difference between $f$-vectors of simplicial and general $d$-polytopes, as well as flag $f$-vectors of $d$-polytopes and…
We study degree sequences for simplicial posets and polyhedral complexes, generalizing the well-studied graphical degree sequences. Here we extend the more common generalization of vertex-to-facet degree sequences by considering arbitrary…
We characterize the cd-indices of Gorenstein* posets of rank 5, equivalently the flag f-vectors of Gorenstein* order complexes of dimension 3. As a corollary, we characterize the f-vectors of Gorenstein* order complexes in dimensions 3 and…
A matroid complex is a pure complex such that every restriction is again pure. It is a long-standing open problem to classify all possible $h$-vectors of such complexes. In the case when the complex has dimension 1 we completely resolve…
Several recent papers have addressed the problem of characterizing the $f$-vectors of cubical polytopes. This is largely motivated by the complete characterization of the $f$-vectors of simplicial polytopes given by Stanley, Billera, and…
Stanley conjectured in 1977 that the $h$-vector of a matroid simplicial complex is a pure $O$-sequence. We give simple constructive proofs that the conjecture is true for matroids of rank less than or equal to 3, and corank 2. We used…