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1.
Richard P. Stanley 《Graphs and Combinatorics》1987,3(1):55-66
I. Bárány and L. Lovász [Acta Math. Acad. Sci. Hung.40, 323–329 (1982)] showed that ad-dimensional centrally-symmetric simplicial polytopeP has at least 2
d
facets, and conjectured a lower bound for the numberf
i
ofi-dimensional faces ofP in terms ofd and the numberf
0 =2n of vertices. Define integers
A. Björner conjectured (unpublished) that
(which generalizes the result of Bárány-Lovász sincef
d–1
= h
i
), and more strongly that
, which is easily seen to imply the conjecture of Bárány-Lovász. In this paper the conjectures of Björner are proved.Partially supported by NSF grant MCS-8104855. The research was performed when the author was a Sherman Fairchild Distinguished Scholar at Caltech. 相似文献
2.
ThisresearchissupportedbytheNationalNaturalScienceFoundationofChina.1.IntroductionInthispaper,weconsiderthefollowinginitial--boundaryvalueproblemwhereQ~fix(o,co),aQ=aflx(o,co),fiisaboundeddomaininEuclideanspaceR"(n22)withsmoothboundaryonandac=(u.,,'Iu..)denotesthegradientoffunctionu(x).Weassumethefunctionsal(x,t,u,p)(i=1,2,',n)anda(x,t,u,p)arelocallyH5ldercontinuousonfix(0,co)suchthatwherealtuandparepositiveconstants,m,aZIa3.hi,b2,alIadZ20,or321areconstants,m*E[0,m 2),hi16z/0,afl m*/… 相似文献
3.
Letn>1. The number of all strictly increasing selfmappings of a 2n-element crown is
. The number of all order-preserving selfmappings of a 2n-element crown is
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4.
Christian Buchta 《Journal of Theoretical Probability》1990,3(3):387-393
Denote byV
n
(d)
the expected volume of the convex hull ofn points chosen independently according to a given probability measure in Euclideand-spaceE
d. Ifd=2 ord=3 and is the measure corresponding to the uniform distribution on a convex body inE
d, Affentranger and Badertscher derived that
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