Jochanan Schönheim, also written Johanan Schonheim, is a mathematician who worked on combinatorics, coverings and group theory. His 1964 paper On Coverings in the Pacific Journal of Mathematics studies collections of k-element subsets of an n-element set in which every l-element subset is covered, a problem going back to Steiner and Moore, and links such coverings to tactical configurations. With Marcel Herzog he posed in 1974 the Herzog-Schönheim conjecture, which says that when a group is partitioned into cosets of subgroups, the indices of the cosets cannot all be different; later work on the problem for free and finitely generated groups still carries both names.
Connections
Conjectures Posed
Source Herzog-Schonheim Conjecture (Wikipedia)
In Branch
Source On Coverings by Johanan Schonheim (Pacific Journal of Mathematics, 1964)
Sources
On Coverings by Johanan Schonheim (Pacific Journal of Mathematics, 1964)
In Branch: Combinatorics, IntroductionQuote, In Branch: Combinatorics, Introduction
renewed interest has been aroused in the notion of covering and related problems
Herzog-Schonheim Conjecture (Wikipedia)
Wikimedia FoundationConjectures Posed: Herzog-Schonheim Conjecture, LeadQuote, Conjectures Posed: Herzog-Schonheim Conjecture, Lead
posed by Marcel Herzog and Jochanan Sch
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