Jonathan Browder
YOU?
Author Swipe
View article: Bucshbaum simplicial posets
Bucshbaum simplicial posets Open
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 B…
View article: A classification of the face numbers of Buchsbaum simplicial posets
A classification of the face numbers of Buchsbaum simplicial posets Open
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 B…
View article: Cellular Resolutions of Ideals Defined by Simplicial Homomorphisms
Cellular Resolutions of Ideals Defined by Simplicial Homomorphisms Open
In this paper we introduce the class of ordered homomorphism ideals and prove that these ideals admit minimal cellular resolutions constructed as homomorphism complexes. As a key ingredient of our work, we introduce the class of cointerval…
View article: Face Numbers of Certain Cohen-Macaulay Flag Complexes
Face Numbers of Certain Cohen-Macaulay Flag Complexes Open
We show that if a $d$-dimensional Cohen-Macaulay complex is, in a certain sense, sufficiently "close" to being balanced, then there is a $d$-dimensional balanced Cohen-Macaulay complex having the same $f$-vector. This in turn provides some…
View article: Lower Bounds for Buchsbaum* Complexes
Lower Bounds for Buchsbaum* Complexes Open
The class of $(d-1)$-dimensional Buchsbaum* simplicial complexes is studied. It is shown that the rank-selected subcomplexes of a (completely) balanced Buchsbaum* simplicial complex are also Buchsbaum*. Using this result, lower bounds on t…
View article: Face numbers of generalized balanced Cohen-Macaulay complexes
Face numbers of generalized balanced Cohen-Macaulay complexes Open
A common generalization of two theorems on the face numbers of Cohen-Macaulay (CM, for short) simplicial complexes is established: the first is the theorem of Stanley (necessity) and Bjorner-Frankl-Stanley (sufficiency) that characterizes …
View article: Shellable Complexes from Multicomplexes
Shellable Complexes from Multicomplexes Open
Suppose a group $G$ acts properly on a simplicial complex $Γ$. Let $l$ be the number of $G$-invariant vertices and $p_1, p_2, ... p_m$ be the sizes of the $G$-orbits having size greater than 1. Then $Γ$ must be a subcomplex of $Λ= Δ^{l-1}*…
View article: Representations of cyclic groups acting on complete simplicial fans
Representations of cyclic groups acting on complete simplicial fans Open
Let $sigma$ be a complete simplicial fan in finite dimensional real Euclidean space $V$, and let $G$ be a cyclic subgroup of $GL(V)$ which acts properly on $σ$. We show that the representation of $G$ carried by the cohomology of $X_{sigma}…