Ed Swartz - Papers
Matroids and quotients of spheres, Math. Zeit., 241 (2002), 247-269.     pdf file

g-elements of matroid complexes, Journal of Comb. Theory Ser. B, 88 (2003), 369-375. pdf file

Lower bounds for h-vectors of k-CM, independence and broken circuit complexes, SIAM J. Disc. Math., 18 (2004/05), 647-661. pdf file

Topological representations of matroid, J. Amer. Math. Soc., 16 (2003), 427-442.  pdf file

(with Tamas Hausel)  Intersection forms of toric hyperkaehler varieties, Proc. Amer. Math. Soc., 134 (2006), 2403-2409   math.AG/0306369

(with Kathryn Nyman)  Inequalities for the h- and flag h-vecotrs of geometric lattices, Disc. and Comp. Geom., 32 (2004), 533-548.  pdf file

g-elements, finite buildings and higher Cohen-Macaulay connectivity, J. Combin. Theory Ser. A, 113 (2006), 1305-1320. math.CO/0512086

Face enumeration: from spheres to manifolds. To appear J. Eur. Math. Soc. math/0709.3998

(with I. Novik)  Face ring multiplicity via CM-connectivity sequences,  To appear, J. Can. Math. Soc., arXive:math.AC/0606.5246

(with P. Hersh) Coloring complexes and arrangements, J. Algebraic Comb., 27 (2008), 205-214. arXive/math/0706.3657

(with J.Chestnut and J. Sapir)  Enumerative properties of triangulations of spherical bundles over S^1, European J. Comb., 29 (2008), 662-671. arXive:math.CO/0611.5039

(with I. Novik)  Socles of Buchsbaum modules, complexes and posets  arXive: mathCO/0711.0783

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 complexes and posets. In particular, new necessary conditions on face numbers and Betti numbers of such complexes and posets are established. These conditions are used to settle in the affirmative Kühnel's conjecture for the maximum value of the Euler characteristic of a 2k-dimensional simplicial manifold on n vertices as well as Kalai's conjecture providing a lower bound on the number of edges of a simplicial manifold in terms of its dimension, number of vertices, and the first Betti number.

(with I. Novik)  Applications of Dehn-Sommerville relations  pdf file

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 $f$-vectors of an even-dimensional manifold with all but the middle Betti number vanishing, (ii) verify K\"uhnel's conjecture that gives an upper bound on the middle Betti number of a $2k$-dimensional manifold in terms of $k$ and the number of vertices, and (iii) partially prove K\"uhnel's conjecture providing upper bounds on other Betti numbers of odd- and even-dimensional manifolds. For manifolds with boundary, we derive an extension of Klee's Dehn-Sommerville relations and strengthen Kalai's result on the number of their edges.

Topological finiteness for edge-vertex enumeration" pdf file
The number of PL-homeomorphism types of combinatorial manifolds in a fixed dimension with an upper bound on g_2 is finite.

(I. Novik)) Gorenstein rings through face rings of manifolds arXiv:0806.1017
The face ring of a homology manifold (without boundary) modulo a system of parameters and most of its socle is Gorenstein. This is used to prove that Kalai's generalization of the g-conjecture for spheres to manifolds follows from the g-conjecture for spheres.

(with F. Lutz and T. Sulanke) f-vectors of 3-manifolds pdf file
  We provide upper bounds for the smallest g_2 which can be realized by a simplicial triangulaion of a number of 3-manifolds. We give a complete characterization of the possible f-vectors of 20 new three-manifolds. Lastly, we show that the connected sum of real projective 3-space with itself has at least two minimal g-vectors.

Lecture notes from "From Polytopes to Enumeration" pdf file

These are lecture notes from the Park City Undergraduate Summer Session course "From Enumeration to Polytopes" I taught in the summer of 2004.   Beginning with an introduction to the geometry of  polytopes,  we are eventurally led to the Dehn-Sommerville equations, zonotopes, hyperplane arrangements and other applications of Möbius inversion.