Ambrus, GERGELY;
Barany, IMRE;
Frankl, PETER;
Varga, DANIEL;
(2023)
Piercing the Chessboard.
SIAM Journal on Discrete Mathematics
, 37
(3)
pp. 1457-1471.
10.1137/21M146048X.
Preview |
PDF
21m146048x.pdf - Other Download (994kB) | Preview |
Abstract
We consider the minimum number of lines and needed to intersect or pierce, respectively, all the cells of the chessboard. Determining these values can also be interpreted as a strengthening of the classical plank problem for integer points. Using the symmetric plank theorem of K. Ball, we prove that for each . Studying the piercing problem, we show that for , where the upper bound is conjectured to be sharp. The lower bound is proven by using the linear programming method, whose limitations are also demonstrated.
| Type: | Article |
|---|---|
| Title: | Piercing the Chessboard |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/21M146048X |
| Publisher version: | http://dx.doi.org/10.1137/21m146048x |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, cells in a lattice, lines, discrete plank problems, DISCRETE REPRESENTATION, ALGORITHM |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10186957 |
Archive Staff Only
 |
View Item |
