9 citations · 12 across the 5 of their papers we have counts for
8 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…
A centrally symmetric version of the cyclic polytope
Alexander Barvinok, Isabella Novik
We define a centrally symmetric analogue of the cyclic polytope and study its facial structure. We conjecture that our polytopes provide asymptotically the largest number of faces…
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…
Symmetric iterated Betti numbers
Eric Babson, Isabella Novik, Rekha Thomas
We define a set of invariants of a homogeneous ideal in a polynomial ring called the symmetric iterated Betti numbers of . For , the Stanley-Reisner ideal of a simplici…