On a Conjecture of Fox and Kleitman on the Degree of Regularity of a Certain Linear Equation View Full Text


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Chapter Info

DATE

2017

AUTHORS

Sukumar Das Adhikari , Shalom Eliahou

ABSTRACT

Fox and Kleitman proved in 2006 that for any positive integer b, the 2n-variable equation \(x_1+\cdots +x_n - x_{n+1}- \cdots - x_{2n} \ = \ b\) is not 2n-regular. Moreover, they conjectured the existence of an integer \(b_n \ge 1\) such that for \(b=b_n\), this equation is \((2n-1)\)-regular. In this note, we settle the first nontrivial case of the conjecture, namely for \(n=2\), and we propose a slight refinement of it. More... »

PAGES

1-8

References to SciGraph publications

  • 1933-12. Studien zur Kombinatorik in MATHEMATISCHE ZEITSCHRIFT
  • Book

    TITLE

    Combinatorial and Additive Number Theory II

    ISBN

    978-3-319-68030-9
    978-3-319-68032-3

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-68032-3_1

    DOI

    http://dx.doi.org/10.1007/978-3-319-68032-3_1

    DIMENSIONS

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