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DESCRIPTION: It is well known that a line can intersect at most 2 n −1 cell
s of the n × n chessboard. What happens in higher dimensions: how many ce
lls of the d -dimensional [0\, n ]^ d box can a hyperplane intersect? W
e answer this question asymptotically. We also prove the integer analogue o
f the following fact. If K\,L are convex bodies in R ^d and K ⊂ L \
, then the surface area K is smaller than that of L . This is joint work
with Péter Frankl.
DTSTAMP:20220527T143200
DTSTART:20220530T160000
CLASS:PUBLIC
LOCATION:Chemistry building\n Arnimallee 22\n 14195 Berlin \n Hörsaal A
SEQUENCE:0
SUMMARY:Imre Bárány (Rényi Institute\, Budapest): Cells in the box and a hy
perplane
UID:126162459@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/math/dates/colloquium/2022/20220530-C-Baran
y.html
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