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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Generalized Hadwiger numbers for symmetric ovals


Authors: Valentin Boju and Louis Funar
Journal: Proc. Amer. Math. Soc. 119 (1993), 931-934
MSC: Primary 52C15; Secondary 52A10, 52C17
MathSciNet review: 1176065
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Abstract: Some estimations for the "juxtaposition function" $ {h_F}$ and an asymptotic formula for the function $ {h_F}/{h_G}$, where $ F,\;G$ are central symmetric convex bodies, are given. Hadwiger and Grünbaum gave for $ {h_F}(1)$ the bounds $ {n^2} + n \leqslant {h_F}(1) \leqslant {3^n} - 1$. Grünbaum conjectured (and proved for $ n = 2$ in Pacific J. Math. 11 (1961), 215-219) that for every even $ r$ between these bounds there exists in $ {E^n}$ an oval $ F$ such that $ {h_F}(1) = r$. Lower bounds for $ {h_F}$ could be derived in the same way as in Theorems 1 and 2 from a good estimate of packing numbers on a Minkowski sphere, that is, from solutions to a Tammes-type problem in a Banch space.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1176065-5
PII: S 0002-9939(1993)1176065-5
Article copyright: © Copyright 1993 American Mathematical Society