About: Let G be a group and [Formula: see text],..., [Formula: see text] be subgroups of G of indices [Formula: see text] respectively. In 1974, M. Herzog and J. Schönheim conjectured that if [Formula: see text], [Formula: see text], is a coset partition of G, then [Formula: see text] cannot be distinct. In this paper, we present a new approach to the Herzog-Schönheim conjecture based on automata and present a translation of the conjecture as a problem on automata.   Goto Sponge  NotDistinct  Permalink

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  • Let G be a group and [Formula: see text],..., [Formula: see text] be subgroups of G of indices [Formula: see text] respectively. In 1974, M. Herzog and J. Schönheim conjectured that if [Formula: see text], [Formula: see text], is a coset partition of G, then [Formula: see text] cannot be distinct. In this paper, we present a new approach to the Herzog-Schönheim conjecture based on automata and present a translation of the conjecture as a problem on automata.
subject
  • Basic concepts in set theory
  • Group theory
  • Combinatorics
  • Conjectures
  • Set families
  • Combinatorial group theory
  • Unsolved problems in mathematics
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