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## Filters

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Extended convex hull

2001
*
Computational geometry
*

Our method applies the

doi:10.1016/s0925-7721(01)00032-3
fatcat:ehcccpjpifdnxeo4hnrskmmxny
*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. ...##
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Monotonicity of the cd-index for polytopes

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

doi:10.1007/s002090050480
fatcat:7cwpw3mk7vdgzdu2ohwbye77ba
*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. ...##
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Two Decompositions in Topological Combinatorics with Applications to Matroid Complexes

1997
*
Transactions of the American Mathematical Society
*

We also introduce a decomposition property

doi:10.1090/s0002-9947-97-01921-1
fatcat:3sfl6u3qjbdvrpucpo56y6dngy
*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. ...##
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On the Korn interpolation and second inequalities in thin domains
[article]

2018
*
arXiv
*
pre-print

being fulfilled

arXiv:1709.04572v5
fatcat:uthtaxcpcjgebixvbh437i2an4
*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. ...##
###
h-Assignments of simplicial complexes and reverse search

2006
*
Discrete Applied Mathematics
*

We propose a practical method that decides shellability of simplicial complexes based on

doi:10.1016/j.dam.2005.09.006
fatcat:3rmtnc2lqva2topl63sdj6gehe
*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 ...##
###
Angle sums of simplicial polytopes
[article]

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*. ...

##
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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

2011
*
Rocky Mountain Journal of Mathematics
*

We investigate the conjectured sufficiency of a condition

doi:10.1216/rmj-2011-41-6-1939
fatcat:2hfecczlz5g6zcxlhxgoxeyqcq
*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). ...##
###
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

2015
*
Bulletin of the American Mathematical Society
*

Among the many consequences of the Brunn-Minkowski theory, let us mention the

doi:10.1090/s0273-0979-2015-01490-4
fatcat:6ew5wsl4kjgrvciyk2gub6ltnu
*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. ...##
###
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. ...

##
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The cd-Index: A Survey
[article]

2020
*
arXiv
*
pre-print

The paper discusses

arXiv:1901.04939v2
fatcat:ny7333qmyrf3dl64hjt3y4moju
*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 ...##
###
Thin-shell concentration for convex measures

2014
*
Studia Mathematica
*

It leads to a Berry-Esseen type estimate

doi:10.4064/sm223-2-2
fatcat:7ejfwv7lrnafpmyyzviwsxv4zy
*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). ...##
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On how to Produce Entangled States Violating Bell's Inequalities in Quantum Theory
[article]

1998
*
arXiv
*
pre-print

Search

arXiv:quant-ph/9810071v2
fatcat:qt65tijnzrbfxphx6nxauoicea
*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. ...##
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Lifting inequalities for polytopes

2005
*
Advances in Mathematics
*

We present a method of lifting linear

doi:10.1016/j.aim.2004.05.005
fatcat:njhswhuxxbg67abutnfftevs7u
*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. ...
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