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math.CO2020
The VC-Dimension of Axis-Parallel Boxes on the Torus
Pierre Gillibert, Thomas Lachmann, Clemens Müllner
We show in this paper that the VC-dimension of the family of -dimensional axis-parallel boxes and cubes on the -dimensional torus are both asymptotically . This…
math.CO2009
An infinite combinatorial statement with a poset parameter
Pierre Gillibert, Friedrich Wehrung
We introduce an extension, indexed by a partially ordered set P and cardinal numbers k,l, denoted by (k,l)-->P, of the classical relation (k,n,l)--> r in infinite combinatorics. By…