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  Volume 8, Issue 2, Article 34
Inequalities on Well-Distributed Point Sets on Circles

    Authors: Alexander Engström,  
    Keywords: Circle, Real roots, Claw-free.  
    Date Received: 04/06/07  
    Date Accepted: 10/06/07  
    Subject Codes:


    Editors: Constantin P. Niculescu,  

The setting is a finite set $ P$ of points on the circumference of a circle, where all points are assigned non-negative real weights $ w(p)$. Let $ P_i$ be all subsets of $ P$ with $ i$ points and no two distinct points within a fixed distance $ d$. We prove that $ W_k^2geq W_{k+1}W_{k-1}$ where $ W_k=sum_{Ain P_i}prod_{pin A} w(p)$. This is done by first extending a theorem by Chudnovsky and Seymour on roots of stable set polynomials of claw-free graphs.

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