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pro vyhledávání: '"Swartz, Ed"'
Given a subgroup $\mathcal{H}$ of a product of finite groups $\mathcal{G} = \displaystyle\prod^n_{i=1} \Gamma_i$ and $b>1,$ we define a polymatroid $P(\mathcal{H},b).$ If all of the $\Gamma_i$ are isomorphic to $\mathbb{Z}/p\mathbb{Z},$ $p$ a prime,
Externí odkaz:
http://arxiv.org/abs/2402.17582
Autor:
Novik, Isabella, Swartz, Ed
We extend several $g$-type theorems for connected, orientable homology manifolds without boundary to manifolds with boundary. As applications of these results we obtain K\"uhnel-type bounds on the Betti numbers as well as on certain weighted sums of
Externí odkaz:
http://arxiv.org/abs/1909.06729
Autor:
Basak, Biplab, Swartz, Ed
Publikováno v:
Advances in Mathematics 365 (2020) 107035
Let $\Delta$ be a $d$-dimensional normal pseudomanifold, $d \ge 3.$ A relative lower bound for the number of edges in $\Delta$ is that $g_2$ of $\Delta$ is at least $g_2$ of the link of any vertex. When this inequality is sharp $\Delta$ has relativel
Externí odkaz:
http://arxiv.org/abs/1803.08942
Autor:
Swartz, Ed
It has been 35 years since Stanley proved that f-vectors of boundaries of simplicial polytopes satisfy McMullen's conjectured g-conditions. Since then one of the outstanding questions in the realm of face enumeration is whether or not Stanley's proof
Externí odkaz:
http://arxiv.org/abs/1411.0987
Autor:
Swartz, Ed
Discrete normal surfaces are normal surfaces whose intersection with each tetrahedron of a triangulation has at most one component. They are also natural Poincar\'e duals to 1-cocycles with $\ZZ/2\ZZ$-coefficients. For a fixed cohomology class in a s
Externí odkaz:
http://arxiv.org/abs/1310.1991
Autor:
Hughes, Marisa J., Swartz, Ed
We consider quotients of spheres by linear actions of real tori. To each quotient we associate a matroid built out of a diagonalization of the torus action. We find the integral homology groups of the resulting quotient spaces in terms of the Tutte p
Externí odkaz:
http://arxiv.org/abs/1205.6387
Autor:
Novik, Isabella, Swartz, Ed
We investigate the face numbers of simplicial complexes with Buchsbaum vertex links, especially pseudomanifolds with isolated singularities. This includes deriving Dehn-Sommerville relations for pseudomanifolds with isolated singularities and establi
Externí odkaz:
http://arxiv.org/abs/1004.5100
Autor:
Klivans, Caroline J., Swartz, Ed
We prove that for any finite real hyperplane arrangement the average projection volumes of the maximal cones is given by the coefficients of the characteristic polynomial of the arrangement. This settles the conjecture of Drton and Klivans that this
Externí odkaz:
http://arxiv.org/abs/1001.5095
The face ring of a simplicial complex modulo m generic linear forms is shown to have finite local cohomology if and only if the link of every face of dimension m or more is `nonsingular', i.e., has the homology of a wedge of spheres of the expected d
Externí odkaz:
http://arxiv.org/abs/1001.2812