Complexes from Complexes

From Flag Complexes to Banner Complexes

A notion of an i-banner simplicial complex is introduced. For various values of i, these complexes interpolate between the class of flag complexes and the class of all simplicial complexes. Examples of simplicial spheres of an arbitrary dimension that are (i+1)-banner but not i-banner are constructed. It is shown that several theorems for flag complexes have appropriate i-banner analogues. Amon...

Bidentate Schiff Base derived from quinolone Ligands Oxovanadium (IV) Complexes

RIGID DUALIZING COMPLEXES

Let $X$ be a sufficiently nice scheme. We survey some recent progress on dualizing complexes. It turns out that a complex in $kinj X$ is dualizing if and only if tensor product with it induces an equivalence of categories from Murfet's new category $kmpr X$ to the category $kinj X$. In these terms, it becomes interesting to wonder how to glue such equivalences.

Shellable complexes from multicomplexes

Suppose a group G acts properly on a simplicial complex Γ . Let l be the number of G-invariant vertices, and p1,p2, . . . , pm be the sizes of the G-orbits having size greater than 1. Then Γ must be a subcomplex of Λ = Δl−1 ∗ ∂Δp1−1 ∗ · · · ∗ ∂Δpm−1. A result of Novik gives necessary conditions on the face numbers of Cohen–Macaulay subcomplexes of Λ. We show that these conditions are also suffi...

Chessboard Complexes and Matching Complexes