language-icon Old Web
English
Sign In

Differences of Bijections

2019 
AbstractWhen is a function from an abelian group to itself expressible as a difference of two bijections? Answering this question for finite cyclic groups solves a problem about juggling. A theorem of Marshall Hall settles the question for finite abelian groups, and a forgotten theorem of Laszlo Fuchs settles the question for infinite abelian groups. After explicating these theorems, we extend the problem by examining expressibility as a difference of injections or surjections. We also extend the question beyond the realm of group theory, where the expressibility of a function translates to questions about partial transversals in Latin squares.
    • Correction
    • Source
    • Cite
    • Save
    • Machine Reading By IdeaReader
    8
    References
    1
    Citations
    NaN
    KQI
    []