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- University of California, BerkeleyUS61 papers
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12 papers · 1 filter
Applications of Klee's Dehn-Sommerville relations
Isabella Novik, Ed Swartz
We use Klee's Dehn-Sommerville relations and other results on face numbers of homology manifolds without boundary to (i) prove Kalai's conjecture providing lower bounds on the f-ve…
Socles of Buchsbaum modules, complexes and posets
Isabella Novik, Ed Swartz
The socle of a graded Buchsbaum module is studied and is related to its local cohomology modules. This algebraic result is then applied to face enumeration of Buchsbaum simplicial…
Expansion properties of a random regular graph after random vertex deletions
Catherine Greenhill, Fred B. Holt, Nicholas Wormald
We investigate the following vertex percolation process. Starting with a random regular graph of constant degree, delete each vertex independently with probability p, where p=n^{-a…
Reverse Lexicographic and Lexicographic Shifting
Eric Babson, Isabella Novik, Rekha R. Thomas
A short new proof of the fact that all shifted complexes are fixed by reverse lexicographic shifting is given. A notion of lexicographic shifting, $Δ_{\lex}$ -- an operation that t…
How neighborly can a centrally symmetric polytope be?
Nathan Linial, Isabella Novik
We show that there exist k-neighborly centrally symmetric d-dimensional polytopes with 2(n+d) vertices, where k(d,n)=Theta(d/(1+log ((d+n)/d))). We also show that this bound is tig…
Proof of the Lovasz Conjecture
Eric Babson, Dmitry N. Kozlov
To any two graphs G and H one can associate a cell complex Hom(G,H) by taking all graph multihomorphisms from G to H as cells. In this paper we prove the Lovasz Conjecture which st…