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DCG
1999
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13 years 9 months ago
Piles of Cubes, Monotone Path Polytopes, and Hyperplane Arrangements
Monotone path polytopes arise as a special case of the construction of fiber polytopes, introduced by Billera and Sturmfels. A simple example is provided by the permutahedron, whic...
Christos A. Athanasiadis
COMPGEOM
2003
ACM
14 years 2 months ago
Long monotone paths in line arrangements
We show how to construct an arrangement of n lines having a monotone path of length Ω(n2−(d/ √ log n)), where d > 0 is some constant, and thus nearly settle the long stan...
József Balogh, Oded Regev, Clifford D. Smyt...