TY - JOUR
T1 - ILLUMINATION of CONVEX BODIES with MANY SYMMETRIES
AU - Tikhomirov, Konstantin
N1 - Publisher Copyright:
Copyright © University College London 2017.
PY - 2017
Y1 - 2017
N2 - Let for a large universal constant 0> and let be a convex body in such that for any , any choice of signs and for any permutation on elements, we have . We show that if is not a cube, then can be illuminated by strictly less than sources of light. This confirms the Hadwiger-Gohberg-Markus illumination conjecture for unit balls of -symmetric norms in for all sufficiently large .
AB - Let for a large universal constant 0> and let be a convex body in such that for any , any choice of signs and for any permutation on elements, we have . We show that if is not a cube, then can be illuminated by strictly less than sources of light. This confirms the Hadwiger-Gohberg-Markus illumination conjecture for unit balls of -symmetric norms in for all sufficiently large .
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U2 - 10.1112/S0025579316000292
DO - 10.1112/S0025579316000292
M3 - Article
AN - SCOPUS:85040771714
SN - 0025-5793
VL - 63
SP - 372
EP - 382
JO - Mathematika
JF - Mathematika
IS - 2
ER -