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Extended convex hull
2001
Computational geometry
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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
2000
Mathematische Zeitschrift
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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
1997
Transactions of the American Mathematical Society
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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]
2018
arXiv
pre-print
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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 for ∈ H^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
2006
Discrete Applied Mathematics
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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]
2020
arXiv
pre-print
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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
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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
2011
Rocky Mountain Journal of Mathematics
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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
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,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
2015
Bulletin of the American Mathematical Society
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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
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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]
2020
arXiv
pre-print
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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
2014
Studia Mathematica
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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]
1998
arXiv
pre-print
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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
2005
Advances in Mathematics
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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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