2021/04/14 by Alirio Gómez Gómez, Gómez, Alirio Gómez, Pedro L. Kaufmann +1
Mathematics · #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2104.07136
openalex publication_date 2021/04/14 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We study combinatorial complexity of certain classes of products of intervals in ℝd, from the point of view of Vapnik-Chervonenkis geometry. As a consequence of the obtained results, we conclude that the Vapnik-Chervonenkis dimension of the set of balls in ℓ_∞d -- which denotes \Rd equipped with the sup norm -- equals \lfloor (3d+1)/2\rfloor.