2010/10/31 by Pablo Soberón · 18 citations
Mathematics · #Convex combination #Generalization #Integer (computer science) #Limits and Structures in Graph Theory #Partition (number theory) #Point processes and geometric inequalities #Regular polygon #Stochastic processes and statistical mechanics #math.MG
paper · pdf · doi:10.1112/s0025579311001914
published in Mathematika 58(1), 71-76 (Wiley)
arxiv created 2011/05/12 · openalex publication_date 2011/10/21 · arxiv updated 2012/02/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We prove the following generalization of the ham sandwich theorem, conjectured by Imre Bárány. Given a positive integer k and d nice measures μ1,μ2,…,μd in ℝd such that μi(ℝd)=k for all i, there is a partition of ℝd into k interior-disjoint convex parts C1,C2,…,Ck such that μi (Cj)=1 for all i,j. If k=2, this gives the ham sandwich theorem. This result was proved independently by R. N. Karasev.