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Extended convex hull

Komei Fukuda, Thomas M. Liebling, Christine Lütolf
2001 Computational geometry  
Our method applies the reverse search algorithm to a shelling ordering of the facets of the convex hull.  ...  In this paper we address the problem of computing a minimal representation of the convex hull of the union of k H -polytopes in R d .  ...  Acknowledgements We would like to thank Günter Rote for his suggestions leading to the wrapping method.  ... 
doi:10.1016/s0925-7721(01)00032-3 fatcat:ehcccpjpifdnxeo4hnrskmmxny

Monotonicity of the cd-index for polytopes

Louis J. Billera, Richard Ehrenborg
2000 Mathematische Zeitschrift  
We prove that the cd-index of a convex polytope satisfies a strong monotonicity property with respect to the cd-indices of any face and its link.  ...  As a consequence, we prove for d-dimensional polytopes a conjecture of Stanley that the cd-index is minimized on the d-dimensional simplex.  ...  We are grateful to Marge Bayer, Tom Braden, Gil Kalai, Margaret Readdy, Günter Ziegler and the referee for comments and corrections on an earlier version of this paper.  ... 
doi:10.1007/s002090050480 fatcat:7cwpw3mk7vdgzdu2ohwbye77ba

Two Decompositions in Topological Combinatorics with Applications to Matroid Complexes

Manoj K. Chari
1997 Transactions of the American Mathematical Society  
We also introduce a decomposition property for simplicial complexes called a convex ear-decomposition, and, using results of Kalai and Stanley on h-vectors of simplicial polytopes, we show that h-vectors  ...  numerical properties for an associated enumerative invariant.  ...  Acknowledgements Thanks to Scott Provan and Neil Stoltzfus for helpful discussions, and to Günter Ziegler and an anonymous referee for a careful reading of earlier versions of the manuscript.  ... 
doi:10.1090/s0002-9947-97-01921-1 fatcat:3sfl6u3qjbdvrpucpo56y6dngy

On the Korn interpolation and second inequalities in thin domains [article]

Davit Harutyunyan
2018 arXiv   pre-print
being fulfilled for practically all thin domains Ω∈ R^3 and all vector fields ∈ H^1(Ω).  ...  We derive Korn's interpolation (or the so called first and a half (The inequality first introduced in [Gra.Har.1])) and second inequalities on that kind of domains forH^1 vector fields, imposing no  ...  The proof is derived from Korn's first inequality on D for an appropriately chosen vector field U ∈ H 1 (D). It is divided into two steps. Step 1. Korn's first inequality on D.  ... 
arXiv:1709.04572v5 fatcat:uthtaxcpcjgebixvbh437i2an4

h-Assignments of simplicial complexes and reverse search

Sonoko Moriyama, Masahiro Hachimori
2006 Discrete Applied Mathematics  
We propose a practical method that decides shellability of simplicial complexes based on reverse search, which improves an earlier attempt by Moriyama, Nagai and Imai.  ...  There is currently no efficient algorithm for deciding whether a given simplicial complex is shellable.  ...  Inspired from the relation between h-vectors and shellings, an h-assignment is defined as follows [4] .An h-assignment is an assignment of a label i with 0 i d + 1 to each facet such that the number of  ... 
doi:10.1016/j.dam.2005.09.006 fatcat:3rmtnc2lqva2topl63sdj6gehe

Angle sums of simplicial polytopes [article]

Sebastian Manecke
2020 arXiv   pre-print
For simplicial polytopes, Dehn-Sommerville-type relations on the α-vector were introduced by Sommerville (1927) and Höhn (1953).  ...  Camenga (2006) defined the γ-vector, a linear transformation analogous to the h-vector and conjectured it to be non-negative.  ...  in the forward and at the entry f d−2 (Θ k ) in the reverse shelling.  ... 
arXiv:2007.07050v1 fatcat:mhsfmdlornabreww6pdmc3yws4

Page 2766 of Mathematical Reviews Vol. , Issue 97E [page]

1997 Mathematical Reviews  
97e:05059 97e:05059 05B35 Chari, Manoj K. (1-LAS; Baton Rouge, LA) Reversible shellings and an inequality for h-vectors. (English summary) Discrete Math. 159 (1996), no. 1-3, 255-259.  ...  We prove that the h-vectors of such reversibly shellable complexes of rank d which have an empty boundary must satisfy the inequality Ay + A, +---+ hy < hg +hg—\ +++++ha_; for i <[d/2].  ... 

On the numbers of faces of low-dimensional regular triangulations and shellable balls

Carl W. Lee, Laura Schmidt
2011 Rocky Mountain Journal of Mathematics  
We investigate the conjectured sufficiency of a condition for h-vectors (1, h 1 , h 2 , . . . , h d , 0) of regular d-dimensional triangulations.  ...  We first prove that the condition is sufficient when h 1 ≥ h 2 ≥ · · · ≥ h d . We then derive some new shellings of squeezed spheres and use them to prove that the condition is sufficient when d = 3.  ...  When we reverse shelling order #2 and create shelling order #3, we are able to construct some h-vectors for which h 3 > h 2 , such as (1, 3, 3, 4, 0, 0, 0, 0).  ... 
doi:10.1216/rmj-2011-41-6-1939 fatcat:2hfecczlz5g6zcxlhxgoxeyqcq

Page 351 of Mathematical Reviews Vol. , Issue 99a [page]

1991 Mathematical Reviews  
,u) is the unit normal vector to this middle surface in the point r(u!,u?) and h = h(u',u?) is the thickness of the shell.  ...  —K), where H and K stand for the mean and Gaussian curvature of the surface, respectively, and f is a real smooth function defined on the interval [—e,00), € > 0, which satisfies the inequality 47f7(r)  ... 

Book Review: Geometry of isotropic convex bodies

Bo'az Klartag
2015 Bulletin of the American Mathematical Society  
Among the many consequences of the Brunn-Minkowski theory, let us mention the reverse Hölder inequalities, proven by Berwald in the 1940s and Borell in the 1970s, stating that for any convex body K ⊆ R  ...  This problem is now largely resolved, thanks to the following central limit theorem for convex sets from 2006: Let X be a random vector in R n that is distributed uniformly in an isotropic convex body.  ... 
doi:10.1090/s0273-0979-2015-01490-4 fatcat:6ew5wsl4kjgrvciyk2gub6ltnu

Page 4070 of Mathematical Reviews Vol. , Issue 89G [page]

1989 Mathematical Reviews  
For certain models of elastic crystals (having a “large” symmetry group) she deduces that QW(F) = h(det F) for some function A. Related conclusions have been obtained by M. Chipot and D.  ...  The authors first derive the full system of equations and boundary conditions for the static problem of the moment theory of shells due to Vekua.  ... 

The cd-Index: A Survey [article]

Margaret M. Bayer
2020 arXiv   pre-print
The paper discusses inequalities on the cd-index, connections with other combinatorial parameters, computation, and algebraic approaches.  ...  The cd-index is an encoding of the numbers of chains, specified by ranks, in the poset.  ...  The authors also described one-sided ideals of the graded algebra A representing flag vector relations on simplicial polytopes and on cubical polytopes, and gave dimension arguments from the resulting  ... 
arXiv:1901.04939v2 fatcat:ny7333qmyrf3dl64hjt3y4moju

Thin-shell concentration for convex measures

Matthieu Fradelizi, Olivier Guédon, Alain Pajor
2014 Studia Mathematica  
It leads to a Berry-Esseen type estimate for most of their one dimensional marginal distributions. We also establish sharp reverse Hölder inequalities for s-concave measures.  ...  We prove that for s < 0, s-concave measures on R n satisfy a thinshell concentration similar to the log-concave case.  ...  As in [18] , an important ingredient in the proof of the thin-shell concentration inequality is an estimate from above of the log-Lipschitz constant of the map on SO(n) : u → h k,p (u).  ... 
doi:10.4064/sm223-2-2 fatcat:7ejfwv7lrnafpmyyzviwsxv4zy

On how to Produce Entangled States Violating Bell's Inequalities in Quantum Theory [article]

Apoorva Patel
1998 arXiv   pre-print
Search for an evolution kernel that cannot be conveniently made non-negative leads to effective interactions that violate time reversal invariance.  ...  This observation emphasises the link between violation of Bell's inequalities in quantum mechanics and unitarity of the theory.  ...  is responsible for correlations violating Bell's inequalities, while "h = 0" is responsible for non-locality.  ... 
arXiv:quant-ph/9810071v2 fatcat:qt65tijnzrbfxphx6nxauoicea

Lifting inequalities for polytopes

Richard Ehrenborg
2005 Advances in Mathematics  
We present a method of lifting linear inequalities for the flag f -vector of polytopes to higher dimensions.  ...  Known inequalities that can be lifted using this technique are the non-negativity of the toric g-vector and that the simplex minimizes the cd-index.  ...  I also thank the Institute for Advanced Study where the calculations were carried out. The author also thanks Margaret Readdy for many helpful suggestions and the two referees for useful comments.  ... 
doi:10.1016/j.aim.2004.05.005 fatcat:njhswhuxxbg67abutnfftevs7u
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